Section: New Results

Statistical aspects of Determinantal Point Processes

Participant : Frédéric Lavancier.

Determinantal point processes (DPPs) have been introduced in their general form by Macchi (1975) and have been extensively studied from a probabilistic point of view in the 2000’s (one of the main reason being their central role in random matrix theory). In a previous work, we have demonstrated that DPPs provide useful models for the description of spatial point pattern datasets where nearby points repel each other.

In [15], we have addressed the question of how repulsive a stationary DPP can be, in order to assess the range of practical situations this promising class of models may model. We determine the most repulsive DPP (in some sense) and we introduce new parametric families of stationary DPPs that can cover a large range of DPPs, from the stationary Poisson process (the case of no interaction) to the most repulsive DPP. Some theoretical aspects of inference for stationary DPPs are tackled in [13] and [14]. In the former study we establish the Brillinger mixing property of stationary DPPs, a first important step toward asymptotic inference. In the latter contribution, we exploit this result to deduce the consistency and asymptotic properties of contrast estimators for stationary DPPs.

References:  [13] [15] [14]

Collaborators: Christophe Ange Napoléon Biscio (LMJL, University of Nantes),

                          Jesper Möller (Department of Mathematical Sciences, Aalborg University, Denmark),

                          Ege Rubak (Department of Mathematical Sciences, Aalborg University, Denmark).