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New Software and Platforms
New Results
Bilateral Contracts and Grants with Industry
Bibliography


Section: New Results

Theory of point processes

In a joint work with Mir-Omid Haji-Mirsadeghi, Sharif University, Department of Mathematics, F. Baccelli studied a class of non-measure preserving dynamical systems on counting measures called point-maps. This research introduced two objects associated with a point map f acting on a stationary point process Φ:

  • The f-probabilities of Φ, which can be interpreted as the stationary regimes of the action of f on Φ. These probabilities are defined from the compactification of the action of the semigroup of point-map translations on the space of Palm probabilities. The f-probabilities of Φ are not always Palm distributions.

  • The f-foliation of Φ, a partition of the support of Φ which is the discrete analogue of the stable manifold of f, i.e., the leaves of the foliation are the points of Φ with the same asymptotic fate for f. These leaves are not always stationary point processes. There always exists a point-map allowing one to navigate the leaves in a measure-preserving way.

Two papers on the matter available. The first one is under revision for Annals of Probability.