2024Activity reportProject-TeamDYOGENE

6.1.1 Book

1. Random Measures, Point Processes, and Stochastic Geometry  10 This book is centered on the mathematical analysis of random structures embedded in the Euclidean space or more general topological spaces, with a main focus on random measures, point processes, and stochastic geometry. Such random structures have been known to play a key role in several branches of natural sciences (cosmology, ecology, cell biology) and engineering (material sciences, networks) for several decades. Their use is currently expanding to new fields like data sciences. The book was designed to help researchers finding a direct path from the basic definitions and properties of these mathematical objects to their use in new and concrete stochastic models. The theory part of the book is structured to be self-contained, with all proofs included, in particular on measurability questions, and at the same time comprehensive. In addition to the illustrative examples which one finds in all classical mathematical books, the document features sections on more elaborate examples which are referred to as models in the book. Special care is taken to express these models, which stem from the natural sciences and engineering domains listed above, in clear and self-contained mathematical terms. This continuum from a comprehensive treatise on the theory of point processes and stochastic geometry to the collection of models that illustrate its representation power is probably the main originality of this book. The book contains two types of mathematical results: (1) structural results on stationary random measures and stochastic geometry objects, which do not rely on any parametric assumptions; (2) more computational results on the most important parametric classes of point processes, in particular Poisson or Determinantal point processes. These two types are used to structure the book. The material is organized as follows. Random measures and point processes are presented first, whereas stochastic geometry is discussed at the end of the book. For point processes and random measures, parametric models are discussed before non-parametric ones. For the stochastic geometry part, the objects as point processes are often considered in the space of random sets of the Euclidean space. Both general processes are discussed as, e.g., particle processes, and parametric ones like, e.g., Poisson Boolean models of Poisson hyperplane processes. We assume that the reader is acquainted with the basic results on measure and probability theories. We prove all technical auxiliary results when they are not easily available in the literature or when existing proofs appeared to us not sufficiently explicit. In all cases, the corresponding references will always be given.

6.1.2 Some random geometric models

2. Poisson approximation of fixed-degree nodes in weighted random connection models  18 We present a process-level Poisson-approximation result for the degree-$k$ vertices in a highdensity weighted random connection model with preferential-attachment kernel in the unit volume. Our main focus lies on the impact of the left tails of the weight distribution for which we establish general criteria based on their small-weight quantiles. To illustrate that our conditions are broadly applicable, we verify them for weight distributions with polynomial and stretched exponential left tails. The proofs rest on truncation arguments and a recently established quantitative Poisson approximation result for functionals of Poisson point processes.

3. Functional central limit theorem for topological functionals of Gaussian critical points  19 We consider Betti numbers of the excursion of a smooth Euclidean Gaussian field restricted to a rectangular window, in the asymptotics where the window grows to ${ℝ}^d$. With motivations coming from Topological Data Analysis, we derive a functional Central Limit Theorem where the varying argument is the thresholding parameter, under assumptions of regularity and covariance decay for the field and its derivatives. We also show fixed-level CLTs coming from martingale based techniques inspired from the theory of geometric stabilisation, and limiting non-degenerate variance.

4. Large and moderate deviations in Poisson navigations 17 We derive large-and moderate-deviation results in random networks given as planar directed navigations on homogeneous Poisson point processes. In this non-Markovian routing scheme, starting from the origin, at each consecutive step a Poisson point is joined by an edge to its nearest Poisson point to the right within a cone. We establish precise exponential rates of decay for the probability that the vertical displacement of the random path is unexpectedly large. The proofs rest on controlling the dependencies of the individual steps and the randomness in the horizontal displacement as well as renewal-process arguments.

5. Some results on the algebraic Aldous diffusion, Pitman-Yor processes, and shot noise fields theses.fr/s260319 In this thesis, we are interested in three relatively distinct problems in probability theory: (i) A Mecke-type characterization of Pitman-Yor processes with a diffuse base measure, (ii) An extension of the Aldous diffusion on algebraic measure trees, and (iii) Limit theorems for randomly weighted sums, with application to shot noise fields. All of them have in common that they are extensions of already established results, to a setting where a stable law appears. Moreover, they can all be linked to at least two of the following fields: stochastic and random geometry, discrete mathematics, and scaling limits.

6.1.3 Hyperuniformity of point processes

6. Rigidity of random stationary measures and applications to point processes 20 The number rigidity of a point process $𝖯$ entails that for a bounded set $A$ the knowledge of $𝖯$ on $A^c$ a.s. determines $𝖯\left(A\right)$; the $k$-order rigidity means we can recover the moments of $𝖯1_A$ up to order $k$. We show that there is $k$-rigidity if the continuous component $𝗌$ of $𝖯$'s structure factor has a zero of order $k$ in 0, by exploiting a connection with Schwartz' Paley-Wiener theorem for analytic functions of exponential type; these results apply to any random $L^2$ wide sense stationary measure on ${ℝ}^d$ or ${\mathbb{Z}}^d$. In the continuous setting, these local conditions are also necessary if ${𝗌}_{}$ has finitely many zeros, or is isotropic, or at the opposite separable. This explains why no model seems to exhibit rigidity in dimension $d⩾3$, and allows to efficiently recover many recent rigidity results about point processes. In the discrete setting, these results hold provided $\#A>2k$.

We derive new results about models of cluster lattices and give the first example of a stationary point process $𝖯\subset {ℝ}^d$ exhibiting arbitrary low decay of the structure factor in 0, hence arbitrary high order of rigidity. For a continuous Determinantal point process with reduced kernel $\kappa$, $k$-rigidity is equivalent to ${(1-\widehat{{\kappa }^2})}^{-1}$ having a zero of order $2k$ in 0, which answers questions on completeness and number rigidity. We also explore the consequences of these statements in the less tractable realm of Riesz gases

7. Hyperuniformity and optimal transport of point processes  21We examine optimal matchings or transport between two stationary point processes and in particular, from a point process to the (integer) lattice or the Lebesgue measure respectively. The main focus of the article is the implication of hyperuniformity (reduced variance fluctuations in point processes) to optimal transport: in dimension 2, we show that the typical matching cost has finite second moment under a mild logarithmic integrability condition on the reduced pair correlation measure, showing that most planar hyperuniform point processes are $L^2$-perturbed lattices. Our method does not formally require assumptions on the correlation measure or the variance behaviour and it retrieves known sharp bounds for neutral integrable systems such as Poisson processes, and also applies to hyperfluctuating systems. The proof relies on the estimation of the optimal transport cost between point processes restricted to large windows for a well-chosen cost through their Fourier-Stieljes transforms, related to their structure factor. The existence of an infinite matching is obtained through a compactness argument on the space of random measures.

8. Estimating the hyperuniformity exponent of point processes 22We address the challenge of estimating the hyperuniformity exponent $\alpha$ of a spatial point process, given only one realization of it. Assuming that the structure factor $S$ of the point process follows a vanishing power law at the origin (the typical case of a hyperuniform point process), this exponent is defined as the slope near the origin of $logS$. Our estimator is built upon the (expanding window) asymptotic variance of some wavelet transforms of the point process. By combining several scales and several wavelets, we develop a multi-scale, multi-taper estimator $\widehat{\alpha }$. We analyze its asymptotic behavior, proving its consistency under various settings, and enabling the construction of asymptotic confidence intervals for $\alpha$ when $\alpha <d$ and under Brillinger mixing. This construction is derived from a multivariate central limit theorem where the normalisations are non-standard and vary among the components. We also present a non-asymptotic deviation inequality providing insights into the influence of tapers on the bias-variance trade-off of $\widehat{\alpha }$. Finally, we investigate the performance of $\widehat{\alpha }$ through simulations, and we apply our method to the analysis of hyperuniformity in a real dataset of marine algae.

6.1.4 Unimodularity, genealogies and random walks

9. Coupling from the Past for the Null Recurrent Markov Chain 2 The Doeblin Graph of a countable state space Markov chain describes the joint pathwise evolutions of the Markov dynamics starting from all possible initial conditions, with two paths coalescing when they reach the same point of the state space at the same time. Its Bridge Doeblin subgraph only contains the paths starting from a tagged point of the state space at all possible times. In the irreducible, aperiodic, and positive recurrent case, the following results are known: the Bridge Doeblin Graph is an infinite tree that is unimodularizable. Moreover, it contains a single bi-infinite path, which allows one to build a perfect sample of the stationary state of the Markov chain. The present paper is focused on the null recurrent case. It is shown that when assuming irreducibility and aperiodicity again, the Bridge Doeblin Graph is either an infinite tree or a forest made of a countable collection of infinite trees. In the first case, the infinite tree in question has a single end, is not unimodularizable in general, but is always locally unimodular. These key properties are used to study the stationary regime of several measure-valued random dynamics on this Bridge Doeblin Tree. The most important ones are the taboo random dynamics, which admits as steady state a random measure with mean measure equal to the invariant measure of the Markov chain, and the potential random dynamics which is a random extension of the classical potential measure, with a mean measure equal to infinity at every point of the state space.

10. Genealogies Of Records Of Stochastic Processes With Stationary Increments As Unimodular Trees  13 Consider a stationary sequence $X=\left(X_n\right)$ of integer-valued random variables with mean $m\in [-\infty ,\infty ]$. Let $S=\left(S_n\right)$ be the stochastic process with increments $X$ and such that $S_0=0$. For each time $i$, draw an edge from $(i,S_i)$ to $(j,S_j)$, where $j>i$ is the smallest integer such that $S_j\ge S_i$, if such a $j$ exists. This defines the record graph of $X$.

It is shown that if $X$ is ergodic, then its record graph exhibits the following phase transitions when $m$ ranges from $-\infty$ to $\infty$. For $m<0$, the record graph has infinitely many connected components which are all finite trees. At $m=0$, it is either a one-ended tree or a two-ended tree. For $m>0$, it is a two-ended tree.

The distribution of the component of 0 in the record graph is analyzed when $X$ is an i.i.d. sequence of random variables whose common distribution is supported on $\{-1,0,1,...\}$, making $S$ a skip-free to the left random walk. For this random walk, if $m<0$, then the component of 0 is a unimodular typically re-rooted Galton-Watson Tree. If $m=0$, then the record graph rooted at 0 is a one-ended unimodular random tree, specifically, it is a unimodular Eternal Galton-Watson Tree. If $m>0$, then the record graph rooted at 0 is a unimodularised bi-variate Eternal Kesten Tree.

A unimodular random directed tree is said to be record representable if it is the component of 0 in the record graph of some stationary sequence. It is shown that every infinite unimodular ordered directed tree with a unique succession line is record representable. In particular, every one-ended unimodular ordered directed tree has a unique succession line and is thus record representable.

6.2.1 Cellular networks

11. On multiclass spatial birth-and-death processes with wireless-type interactions  9 This paper studies a multiclass spatial birth-and-death (SBD) processes on a compact region of the Euclidean plane modeling wireless interactions. In this model, users arrive at a constant rate and leave at a rate function of the inter- ference created by other users in the network. The novelty of this work lies in the addition of service differentiation, inspired by bandwidth partitioning present in 5G networks: users are allocated a fixed number of frequency bands and only interfere with transmissions on these bands. The first result of the paper is the determination of the critical user arrival rate below which the system is stochastically stable, and above which it is unstable. The analysis requires symmetry assumptions which are defined in the paper. The proof for this result uses stochastic monotonicity and fluid limit models. The monotonicity allows one to bound the dynamics from above and below by two adequate discrete-state Markov jump processes, for which we obtain stability and instability results using fluid limits. This leads to a closed form expression for the critical arrival rate. The second contribution consists in two heuristics to estimate the steady-state densities of all classes of users in the network: the first one relies on a Poisson approximation of the steady-state processes. The second one uses a cavity approximation leveraging second-order moment measures, which leads to more accurate estimates of the steady-state user densities. The Poisson heuristic also gives a good estimate for the critical arrival rate.

12. Spatial Network Calculus and Performance Guarantees in Wireless Networks  5 This work develops a novel approach toward performance guarantees for all links in arbitrarily large wireless networks. It introduces a spatial network calculus, consisting of spatial regulation properties for stationary point processes and the first steps of a calculus for this regulation, which can be seen as an extension to space of the classical network calculus. Specifically, two classes of regulations are defined: one includes ball regulation and shot-noise regulation, which are shown to be equivalent and upper constraint interference; the other one includes void regulation, which lower constraints the signal power. These regulations are defined both in the strong and weak sense: the former requires the regulations to hold everywhere in space, whereas the latter only requires the regulations to hold as observed by a jointly stationary point process. Using this approach, we derive performance guarantees in device-to-device, ad hoc, and cellular networks under proper regulations. We give universal bounds on the SINR for all links, which gives link service guarantees based on informationtheoretic achievability. They are combined with classical network calculus to provide end-to-end latency guarantees for all packets in wireless queuing networks. Such guarantees do not exist in networks that are not spatially regulated, e.g., Poisson networks.

6.2.2 Reconfigurable intelligent surfaces (RIS)

13. Reconfigurable Intelligent Surfaces in Cellular Networks: Performance Analysis and Optimal Design 11This thesis investigates the impact of deploying reconfigurable intelligent surfaces (RIS), which can engineer spatial diversity in complex cellular networks, at a system level. We develop a framework to characterize the performance of RIS-assisted cellular networks, focusing on downlink coverage probability and ergodic rate, where we consider that multiple RISs can serve one UE simultaneously. To account for the inherent randomness in the spatial deployment of base stations (BSs) and RISs, we model the placements of the RISs as point processes (PPs) conditioned on the associated BSs, which are modeled by a Poisson point process (PPP). These RIS PPs can be adapted based on the deployment strategy. We focus on modeling the RISs as a Matérn cluster process (MCP), where each RIS cluster is a finite PPP with support of a disc centered on the association BS. We assume that the system uses the orthogonal frequency division multiplexing (OFDM) technique to exploit the multipath diversity provided by RISs. The coverage probability and the ergodic rate can be evaluated when RISs operate as batched powerless beamformers. The resulting analytical expressions provide a general methodology to evaluate the impact of key RIS-related parameters, such as the density of RISs, on system-level performance. To demonstrate the framework's broad applicability, we also analyze a RIS placement variant where RISs are deployed around coverage holes. Furthermore, the proposed framework enables techno-economic analysis of RIS-assisted networks. We introduce a relative cost model considering the total cost of ownership (TCO) of deploying both BSs and RISs, along with a return on investment (RoI) model that is proportional to spectral efficiency. This approach gives operators quantitative insights into the development of investment strategies regarding whether to invest in RISs or BSs based on current BS and RIS densities. To assess performance and conduct techno-economic analysis, the analytical expressions involve multiple integrals which are computationally complex. We address this challenge by developing a novel numerical solver based on the Genz-Malik rule and parallel computing, allowing efficient evaluation within acceptable time consumption and improving the practical applicability of the proposed framework. Based on this solver, numerical evaluations of the analytical expressions and Monte-Carlo simulations jointly validate the proposed analytical approach and provide valuable insights into the design of future RIS-assisted cellular networks.

14. How Much Can Reconfigurable Intelligent Surfaces Augment Sky Visibility: A Stochastic Geometry Approach 7 This paper uses the theory of point processes and stochastic geometry to quantify the sky visibility experienced by users located in an outdoor environment. The general idea is to represent the buildings of this environment as a stationary marked point process, where the points represent the building locations and the marks their heights. The point process framework is first used to characterize the distribution of the blockage angle, which limits the visibility of a typical user into the sky due to the obstruction by buildings. In the context of communications, this distribution is useful when users try to connect to the nodes of an aerial or non-terrestrial network in a Line-of-Sight way. Within this context, the point process framework can also be used to investigate the gain of connectivity obtained thanks to Reconfigurable Intelligent Surfaces. Assuming that such surfaces are installed on the top of buildings to extend the user’s sky visibility, this point process approach allows one to quantify the gain in visibility and hence the gain in connectivity obtained by the typical user. The distributional properties of visibility-related metrics are cross-validated by comparison to simulation results and 3GPP measurements.

15. Shortest Path Lengths in Poisson Line Cox Processes: Approximations and Applications 16 We derive exact expressions for the shortest path length to a point of a Poisson line Cox process (PLCP) from the typical point of the PLCP and from the typical intersection of the underlying Poisson line process (PLP), restricted to a single turn. For the two turns case, we derive a bound on the shortest path length from the typical point and demonstrate conditions under which the bound is tight. We also highlight the line process and point process densities for which the shortest path from the typical intersection under the one turn restriction may be shorter than the shortest path from the typical point under the two turns restriction. Finally, we discuss two applications where our results can be employed for a statistical characterization of system performance: in a re-configurable intelligent surface (RIS) enabled vehicle-to-vehicle (V2V) communication system and in electric vehicle charging point deployment planning in urban streets.

6.2.3 Non-Terrestrial Networks (NTN)

16. Large Satellite Constellations: Challenges and Impact 12The New Space Age (NewSpace) marks the advent of a new era in the use of space, characterized by the opening of space to new players, the use of new space technologies, new functionalities for satellites in orbit, and the development of satellite constellations, mainly in the fields of communications and Earth observation. These developments are underpinned by first-rate scientific and technological advances, as well as considerable public and private investment, in particular in the USA, China and, to a lesser extent, Europe. Fleets of small low- and medium-orbit satellites are replacing or complementing the large geostationary satellites that predominated in the previous period. Whereas space used to be reserved to a small number of states and major industrial groups, one is now witnessing the emergence of new space states, new industrial groups such as SpaceX or Amazon, and many start-ups. One also observes the emergence of companies with launching and satellite manufacturing capacities, which are also taking on the role of telecommunication operators and content producers. The most visible result of the deployment of these new space networks is the ability to provide high-speed, low-latency Internet connections to any point on the globe. Combined with Earth observation capabilities, these new communications resources also enable real-time action to be taken in any region, including those with no equipment other than terminals. In addition, these space networks are remarkably resilient compared with terrestrial networks. Geostrategic and military considerations combine with rapidly evolving business models to explain the massive investments currently being made in this domain. However, the lack of international regulation in the field is leading to a race to occupy orbits and frequencies, which has already had serious consequences for a whole range of scientific activities. These constellations have a potentially negative impact on astronomy in the visible and infrared optical domains, as well as on radio astronomy. They also raise a major problem in terms of space congestion, with an increase in the amounts of satellite debris resulting from launches or collisions between satellites, and the possibility of reaching a phase of chain reaction collisions. In addition, from an environmental point of view, the consequences of the proliferation of launches and uncontrolled re-entries into the atmosphere are equally worrying. What’s more, the lack of regulation in the field also leads to a loss of sovereignty, since these new satellite communication networks do not comply with any of the rules that states impose on terrestrial communication networks operating on their territories. A sustainable, global solution must be found to these problems, before major and potentially irreversible damage is inflicted on the planet’s environment, geostrategic balances, democracy, and science. While the Académie des Sciences considers that France and Europe need to step up their scientific and industrial actions in this field in order to benefit from the remarkable advances of these new networks, and ultimately leverage the benefits of a resilient and secure communications network, the Académie also recommends working in parallel to strengthen regulation of the field with the aim of assuring sustainable access to orbital and frequency resources, as well as protection for negatively impacted fields, foremost among which are astronomy and the environment.

17. Cox Point Processes for Multi Altitude LEO Satellite Networks  3To model existing or future low Earth orbit (LEO) satellite networks leveraging multiple constellations, we propose a simple analytical approach to represent the clustering of satellites on orbits. More precisely, we develop a variable-altitude Poisson orbit process that effectively captures the geometric fact that satellites are always positioned on orbits, and these orbits may vary in altitude. Conditionally on the orbit process, satellites situated on these orbits are modeled as linear Poisson point processes, thereby forming a Cox point process. For this model, we derive useful statistics, including the distribution of the distance from the typical user to its nearest visible satellite, the outage probability, the Laplace functional of the proposed Cox satellite point process, and the Laplace transform of the interference power from the Cox-distributed satellites under general fading. The derived statistics enable the evaluation of the performance of such LEO satellite communication systems as functions of network parameters.

7.1.1 CRE with Orange Labs

Two year contract titled Guaranteed throughput and millimeter waves in the dimensioning of 5G cellular networks between Inria and Orange Labs started 2022 and attached to the joint Inria-Orange lab "IOLab". It is a part of a long-term collaboration between TREC/DYOGENE, represented by B. Błaszczyszyn and Orange Labs, represmnted by M. K. Karray on the development of mathematical methods and engineering analytical tools for the dimensioning of wireless cellular networks enabling operators to solve critical technical and economic issues related to the main business related to the permanent evolution of radio technology. They capture the macroscopic relation between antenna deployment, frequency allocation, the volume of traffic carried on the network, and QoS parameters, such as the average and variation in bandwidth available to end users. The math solutions developed in cooperation with Orange Labs are implemented by Orange Labs in their internal toolbox and used for dimensioning studies by Direction des Affaires Réglementaires of Orange, Orange France in relation to ARCEP (Autorité de Régulation des Communications Électroniques, des Postes et de la Distribution de la Presse) and Orange affiliates. Contract with Orange started in 2023 for the co-advising a PhD student of Orange, Lucas Darlavoix , titled “Machine Learning for QoS evaluation and dimensioning of wireless cellular networks” .

7.1.2 CIFRE with Orange.

Contract with Orange started in 2023 for the co-advising a PhD student of Orange, Lucas Darlavoix , titled “Machine Learning for QoS evaluation and dimensioning of wireless cellular networks” .

7.1.3 CIFRE with Nokia Bell Labs

Contract with Nokia Bell Labs France for the co-advising a PhD student Guodong Sun (2022–24), titled ”Reconfigurable Intelligent Surfaces in Next Generation Wireless Systems: Performance Analysis”;  11.

8.1.1 Alliance Communauto Montreal

Participants: Christine Fricker.

Dyogene (Christine Fricker ) participates in 4-year research project (2023-2027) co-funded by Communauto, NSERC and MItacs in Montreal.

8.1.2 STAR South Korea-France

Participants: François Baccelli, Nahuel Soprano Loto, Philippe Sarotte.

Hubert Curien STAR South Korea-France three-year project (2024-2027), led by François Baccelli on the Inria side and Chang Sik Choi [Hongik University] on the South Korean side, focuses on modeling Non-Terrestrial Networks (NTN) in low Earth orbit using stochastic geometry.

8.2.1 Visits of international scientists

• Ravi Mazumdar , professor at WATERLOO CANADA, until Mar 2024
• Hermann Thorisson , professor at University of Iceland, from Sep 2024 until Nov 2024

8.3.1 ERC NEMO

Participants: François Baccelli, Bartłomiej Błaszczyszyn, Ke Feng, Sayeh Khaniha, Ali Khezeli, Sanjoy Kumar Jhawar, Emanuele Mengoli, Bharath Roy Choudhury, Nahuel Soprano Loto.

ERC NEMO (NEtwork MOtion; cordis.europa.eu, project.inria.fr) is an ERC Advanced Grant (2019 – 2024, PI François Baccelli). It is an inter-disciplinary proposal centered on network dynamics. The inter-disciplinarity spans from communication engineering to mathematics, with an innovative interplay between the two. NEMO’s aim is to introduce dynamics in stochastic geometry. General mathematical tools combining stochastic geometry, random graph theory, and the theory of dynamical systems will be developed. NEMO leverages interactions of Inria with Ecole Normale Supérieure on the mathematical side, and with Nokia Bell Labs and Orange on the engineering side.

8.3.2 SNS INSTINC

Participants: François Baccelli, Emanuele Mengoli, Nahuel Soprano Loto.

A project titled "Joint Communications and Services" within the Smart Networks and Services (SNS) Joint Undertaking, a collaboration between the EU Council and industrial partners aimed at advancing Europe's leadership in 6G technology and accelerating 5G deployment. Inria received funding for its individual program, coordinated by Jean-Marie Gorce at INSA-Lyon, with participation from François Baccelli , Nahuel Soprano Loto , and a research engineer, Emanuele Mengoli .

8.4.1 PEPR "5G et Réseaux du Futur"

Participants: François Baccelli, Bartłomiej Błaszczyszyn, Philippe Sarotte, Nahuel Soprano Loto.

As a part of the national "Programmes et équipements prioritaires de recherche" (PEPR), «5G et Réseaux du Futur» project is led by Institut Mines-Télécom, CEA, and CNRS as the leaders. (Inria is a partner but is not leading this project.) It is made up of 10 projects (PC1 to PC10). (Inria teams are involved in several of these projects.) F. Baccelli and J-M. Gorce carried the PC9 project, which is focused on theoretical tools and fundamental limits. F. Baccelli will be the coordinator of this project, for Inria. The launch took place on July 10-11-12 2023.

8.4.2 PGMO

Participants: Christine Fricker, Alessia Rigonat, Hanene Mohamed.

Project “Charging issues in vehicle-sharing systems: Stochastic modeling and large scale analysis” within the Gaspard Monge Program for optimization, operations research and their interactions with data sciences funded by the Fondation Mathématique Jacques Hadamard (FMJH) led by Christine Fricker .

8.4.3 RT MAIAGES

Participants: All Dyogene/MathNet.

Members of Dyogene were active participants in the Research Group GeoSto (GdR 3477) on Stochastic Geometry. This activity has since been integrated into the Thematic Network MAIAGES, which focuses on Mathematics for Imaging, Learning, and Stochastic Geometry. This integration broadens the scope and fosters new collaboration opportunities.

8.5.1 AEx Smovengo

Participants: Christine Fricker, Raphaël Lachièze-Rey.

An exploratory acction Flow Estimation and Self-Service Vehicle Regulation between Inria and Smovengo Paris was validated in 2024. A contract with this operator of a bike-sharing service is signed at the beginning of 2025.

8.5.2 IA4IDF

Participants: Christine Fricker, Alessia Rigonat.

Contract of three years, started at 2024, with Île-de-France region via the DIM (Domain of Major Interest) program IA4IDF (Artificial Intelligence for Île-de-France) for adwising PhD thesis of Alessia Rigonat on ”Modeling and AI prediction fo car-sharing”.

8.5.3 LINCS

Participants: François Baccelli, Bartłomiej Błaszczyszyn, Some (Post-doc) Students.

The team is also affiliated with the LINCS, a research center co-founded by Inria, Institut Mines-Télécom, UPMC, and Alcatel-Lucent Bell Labs (now Nokia Bell Labs). LINCS focuses on research and innovation in future information and communication networks, systems, and services. Many of our members and students actively participate in selective LINCS activities. Notably, those involved in the communication engineering aspect of ERC NEMO—an interdisciplinary ERC Advanced Grant (2019–2024, PI François Baccelli)— deeply engaged in LINCS initiatives. Students working under CIFRE agreements (Industrial Agreements for Training through Research) with Orange Labs, Nokia Bell Labs, etc, typically spend part of their time at the premises of their industrial employers, fostering strong industry-academia collaborations.

8.6.1 Inria-AP-HP Challenge Urge

Participants: Christine Fricker.

Dyogene participates in the URGE Inria-AP-HP défi on optimisation of care management in emergency departments.

9.1.1 Scientific events: organisation

• Workshop on RIS; International Workshop on RIS (Reconfigurable Intelligent Surfaces) held at LINCS in 2004; organized by François Baccelli .
• Workshop on Hyperuniformity; International workshop on Hyperuniformity and Related Topics, held in at Inria in 2024, focused on mathematical random models of real-world structures. These models are notable for their remarkable properties, such as low variance and intrinsic rigidity exhibited by perturbed lattices. This makes them a fascinating subject for mathematical investigation, with applications spanning various fields, including physics, communications, numerical integration, and more. Organized by Raphaël Lachièze-Rey .
• Seminar DYOGENE organizes weekly scientific seminar which are also available online. Among our speakers are: Sergey Zuyev (University of Gothenburg), Zakhar Kabluchko (University of Münster), Christian Hirch (Aarhus university), Venkat AnantharPaul Pierre Raxam (University of California, Berkeley), Ellen Baake (University of Bielefeld), Giovanni Peccati (Luxembourg University), Julia Gaudio (Northwestern University), Gourab Ghatak (IIT Delhi), MIchel Davydov (Brown University). Organized by Bharath Roy Choudhury and Sanjoy Kumar Jhawar .
• Hermann Thorisson (University of Iceland) weekly teaching at Inria a course on ”Coupling Methods in Probability Theory Session” (September 5th to October 3rd, 2024 and October 24th to November 21st, 2024)

9.1.2 Talks and posters

• François Baccelli
  • Lecture at the French Parliament on satellite constellation based communication networks, February 1, 2024.
  • Invited lecture at the Stochastic Network Conference 2024, Stockholm, Sweden, July 1-5, 2024. “Lecture on unimodular random graphs and evolution”.
  • Plenary lecture on the FOUNDATION project at the Kick-off meeting of the French national research program on communication networks (PEPR RF), Grenoble, March 20-22, 2024.
  • Invited lecture at the Bath conference "Stochastic Geometry in Action", Department of mathematics, Bath University, UK, September 10-13. “Lecture on random graphs”'.
  • Colloquium at Korea University, Seoul, Department of Electrical Engineering, November 25, 2024, talk on wireless stochastic geometry.
  • Colloquium at SNU, Seoul, Department of Electrical Engineering, November 28, 2024, talk on wireless network dynamics.
  • Invited lecture at the 2024 "Atelier d'évaluation de performances", Toulouse, December 2-5, 2024. Talk on random graphs.
• Bartłomiej Błaszczyszyn
  • Doctoral Program in Statistics and Applied Probability, CUSO (Conference of Western Swiss Universities), Summer School, Anzère 24, Switzerland, September 1-4, 2024. “Ergodic Learning of Spatial Geometric Structures”.
  • Invited talk, Workshop on Stochastic Geometry in Action,
  • Talk at Workshop on Hyperuniformity and related topics Inria, Paris, December 11-13, 2024, “Ergodic Learning of Point Processes: From Theory to Practice”.
• Bharath Roy Choudhury
  • Talk at Bernoulli-IMS 11th World Congress in Probability and Statistics, Bochum, Germany, August 2024. “Genealogies of records of stochastic processes with stationary increments as unimodular trees”.
  • Invited talk at Biomathematics and Theoretical Bioinformatics group, Bielefeld university, 23 May 2014. “Unimodular networks and records of stochastic processes with stationary increments”.
  • Invited talk at the probability seminar of the Institute de Mathématiques of Aix-Marseille University, 09 April 2024, Marseille. “Genealogies of records of stochastic processes with stationary increments as unimodular trees”.
  • Poster presentation at Eurandom YEP 2024: “Interplay between local and global graph structures, Eindhoven, 11 Mar 2024 - 15 Mar 2024. “Genealogies of records of stochastic processes with stationary increments as unimodular trees”.
• Ke Feng
  • Invited talk, HUST, Wuhan, China, May 20. “Spatial network calculus and performance guarantees in wireless networks”.
  • Poster session at Bernoulli-IMS 11th World Congress in Probability and Statistics, Bochum, Germany, August 2024. “Spatial Disease Propagation With Hubs”.
• Christine Fricker
  • Invited talk on 13eme atelier en évaluation de performances, Toulouse, December 2-4,  2024. “Approximation of large bike/car sharing systems”.
• Roman Gambelin
  • Talk at Séminaire doctoral du LPSM, of the Laboratoire de Probabilités, Statistique et Modélisation, Sorbonne Université & Université Paris Cité, April 2024. “An extension of the algebraic Aldous diffusion”.
  • Talk at Probability Seminar Essen Semiar at University of Duisburg-Essen, Germany, Janary 2025. “A quantitative central limit theorem for linear functionals of Pitman-Yor processes”.
• Sanjoy Kumar Jhawar
  • Talk at Workshop on Random Graphs, DYOGENE, May 2024. “Large and moderate deviation for Poisson navigations”.
  • Talk at Bernoulli-IMS 11th World Congress in Probability and Statistics, Bochum, Germany, August 2024. “Moderate and large deviation in Poisson navigation”.
  • Talk at DYOGENE Seminar, September 2024. “Handover frequency in dynamic terrestrial network”.
  • Talk at LINCS Seminar, December 2024. “Handover frequency in dynamic terrestrial network”.
• Sayeh Khaniha
  • Oxford Talks, Oxford, UK, January 2024. “Coupling from the Past for the Null Recurrent Markov Chain”'.
  • Stochastic Geometry Days, Tours, France, May 2024. “Hierarchical Mutual Nearest-Neighbor Clustering on Poisson Point Process”'.
  • Poster Presentation, Stochastic Networks Conference, KTH, Stockholm, Sweden. July 2024. “Hierarchical Thinning Nearest Neighbor Algorithm”.
  • Talk at 11th World Congress in Probability and Statistics, Bochum, Germany, August 2024. “Coupling from the Past for the Null Recurrent Markov Chain”
  • Seminar Talk, Dynamics of the Information and Networks Laboratory, EPFL, Switzerland, September 2024. “Hierarchical Clustering on Point Processes”.
• Raphaël Lachièze-Rey
  • Talk at Groningen Probability and Statistics Seminar, Groningen, The Netherlands, March, 2024. “Optimal transport and matching of point processes”.
  • Talk at Probability & Statistics Seminar, University of Luxembourg, May 2024. “Optimal transport and matching of point processes”.
  • Talk at 22nd Workshop on Stochastic Geometry, Stereology and Image Analysis, Bad Herrenalb (Black Forest), Germany, June 2024. “Transport rates for dependent point processes”.
  • Talk at Online Seminar on Spatial and spatio-temporal Point processes and beyond (OSSP), Novembre, 2024. “Hyperuniformity exponent estimation, rigidity and simulation”.
  • Talk at Workshop on Hyperuniformity and related topics Inria, Paris, December 11-13, 2024, “Rigidity of point processes”.
• Gabriel Mastrilli
  • Talk at PhD Days at ENSAI, Rennes, December 2024. “Non asymptotic spectral estimation for spatial point processes”.
  • Talk at 22nd Workshop on Stochastic Geometry, Stereology and Image Analysis, Bad Herrenalb (Black Forest), Germany, June 2024. “Estimating the structure factor exponent at zero-wavelength for hyperuniform point processes”.
  • Talk at DYOGENE Seminar, September 2024. “Estimating the hyperuniformity exponent of spatial point processes”.
• Emanuele Mengoli
  • Talk at 13ème Atelier en Évaluation des Performances, Toulouse, December 2024. “Dynamic Bayesian Optimization for Improving the Performance of Cellular Networks”.
• Alessia Rigonat
  • Talk at Seminaire MODAL’X Modélisation aléatoire de Paris Nanterre, March 2024. “Stochastic averaging for a large system with fast varying environment”.
• Guodong Sun
  • Talk at International Workshop on RIS, LINCS, IMT Saclay, February 2024. “Performance Analysis of RIS-assisted MIMO-OFDM Cellular Networks Based on Matern Cluster Processes”.

9.1.3 Leadership within the scientific community

• Raphaël Lachièze-Rey is a member of the Fondation Sciences Mathématiques de Paris (FSMP) steering committee and the FSMP postdoc jury.
• Raphaël Lachièze-Rey is a member of the Scientific Council of the Laboratory MAP5.

9.1.4 Scientific expertise

Bartłomiej Błaszczyszyn served as a reviewer for an individual project submitted to the German Research Foundation (DFG).

9.1.5 Research administration

François Baccelli is one of the four co-funding members of the new “Centre National Réseaux et Systèmes pour la Transformation Numérique” funded by IMT in 2024.

9.2.1 Teaching

• Licence: B. Błaszczyszyn (Cours) Théorie de l'information et du codage 24 heqTD, L3, ENS Paris. moodle.psl.eu
• Master: B. Błaszczyszyn (Cours) "Random Geometric Models", jointly at M2 “Probabilities and Random Models”, Sorbonne University and M2 “Applied and Theoretical Mathematics”, University Paris-Dauphine-PSL (39heqTD). moodle.psl.eu

9.2.2 Supervision

9.2.3 Juries

• Bartłomiej Błaszczyszyn
  : PhD jury of Claire Bizon Monroc (ENS 2024), Julien Weibel (Université d’Orléans 2024; reviewer).
• Christine Fricker
  : member of the thesis committee of Sebastian Allmeier (INRIA Grenoble).
• Raphaël Lachièze-Rey
  : PhD jury of Laurent Freoa (MAP5 2024).

9.3.1 Specific official responsibilities in science outreach structures

• Two papers of François Baccelli were published in Issue N° 27 of Annales des Mines, September 2024, entitled “Maîtrise de la complexité dans la 6G - L’approche par la géométrie stochastique” and “Réseaux de communications sur constellations de satellites”.
• Raphaël Lachièze-Rey spoke on data analysis at a political science conference at Sciences Po.

International journals

• 1 articleF.François Baccelli, S.Sergey Foss and S.S. Shneer. Migration-Contagion Processes.Advances in Applied Probability5612024, 71-105HALDOIback to text
• 2 articleF.François Baccelli, M.-O.Mir-Omid Haji-Mirsadeghi and S.Sayeh Khaniha. Coupling from the Past for the Null Recurrent Markov Chain.The Annals of Applied Probability344August 2024HALDOIback to text
• 3 articleC.-S.Chang-Sik Choi and F.François Baccelli. Cox Point Processes for Multi Altitude LEO Satellite Networks.IEEE Transactions on Vehicular Technology7310October 2024, 15916-15921HALDOIback to text
• 4 articleG.Guy Fayolle and C.Christine Fricker. Thermodynamical limits for models of car-sharing systems: the Autolib' example.Markov Processes And Related Fields2025, 17In press. HALback to text
• 5 articleK.Ke Feng and F.François Baccelli. Spatial Network Calculus and Performance Guarantees in Wireless Networks.IEEE Transactions on Wireless Communications2352024, 5033-5047HALDOIback to text
• 6 articleC.Christine Fricker and H.Hanene Mohamed. Mean field analysis of stochastic networks with reservation.Journal of Applied ProbabilityJanuary 2025, 1-27HALDOIback to text
• 7 articleJ.Junse Lee and F.François Baccelli. How Much Can Reconfigurable Intelligent Surfaces Augment Sky Visibility: A Stochastic Geometry Approach.IEEE Transactions on Wireless Communications241January 2025, 796-809HALDOIback to text
• 8 articleB.Bianca Marin Moreno, C.Christine Fricker, H.Hanene Mohamed, A.Amaury Philippe and M.Martin Trépanier. An incentive algorithm for a closed stochastic network: data and mean-field analysis.La Matematica32April 2024, 651-676HALDOIback to text
• 9 articleP.Pierre Popineau and F.François Baccelli. On multiclass spatial birth-and-death processes with wireless-type interactions.IEEE Transactions on Information Theory2024, 1-1HALDOIback to text

Scientific books

• 10 bookF.François Baccelli, B.Bartłomiej Błaszczyszyn and M.Mohamed Karray. Random Measures, Point Processes, and Stochastic Geometry.InriaJuly 2024HALback to text

Doctoral dissertations and habilitation theses

• 11 thesisG.Guodong Sun. Reconfigurable Intelligent Surfaces in Cellular Networks: Performance Analysis and Optimal Design.Université Paris Sciences & LettresDecember 2024HALback to textback to textback to text

Reports & preprints

• 12 reportF.François Baccelli, S.Sébastien Candel, G.Guy Perrin and J.-L.Jean-Loup Puget. Large Satellite Constellations: Challenges and Impact.Académie des sciencesMarch 2024HALDOIback to textback to text
• 13 miscF.François Baccelli and B.Bharath Roy Choudhury. Genealogies Of Records Of Stochastic Processes With Stationary Increments As Unimodular Trees.March 2024HALback to text
• 14 miscC.Christine Fricker, H.Hanene Mohamed and A.Alessia Rigonat. Stochastic averaging and mean-field for a large system with fast varying environment with applications to free-floating car-sharing.March 2024HALback to text
• 15 miscC.Christine Fricker, H.Hanene Mohamed, A.Alessia Rigonat and M.Martin Trépanier. A new stochastic model for carsharing suited to free-floating.February 2024HALback to text
• 16 miscG.Gourab Ghatak, S. K.Sanjoy Kumar Jhawar and M.Martin Haenggi. Shortest Path Lengths in Poisson Line Cox Processes: Approximations and Applications.November 2024HALback to text
• 17 miscP. P.Partha Pratim Ghosh, B.Benedikt Jahnel and S. K.Sanjoy Kumar Jhawar. Large and moderate deviations in Poisson navigations.March 2024HALback to text
• 18 miscC.Christian Hirsch, B.Benedikt Jahnel, S. K.Sanjoy Kumar Jhawar and P.Péter Juhász. Poisson approximation of fixed-degree nodes in weighted random connection models.February 2024HALback to text
• 19 miscC.Christian Hirsch and R.Raphaël Lachièze-Rey. Functional central limit theorem for topological functionals of Gaussian critical points.November 2024HALback to text
• 20 miscR.Raphaël Lachièze-Rey. Rigidity of random stationary measures and applications to point processes.February 2025HALback to text
• 21 miscR.Raphaël Lachièze-Rey and D.Dahandapani Yogeshwaran. Hyperuniformity and optimal transport of point processes.February 2024HALback to text
• 22 miscG.Gabriel Mastrilli, B.Bartlomiej Blaszczyszyn and F.Frédéric Lavancier. Estimating the hyperuniformity exponent of point processes.2024HALback to text