Poisson suspensions and Sushis
Probability
2018-01-22 v4 Dynamical Systems
Abstract
In this paper, we prove that ergodic point processes with moments of all orders, driven by particular infinite measure preserving transformations, have to be a superposition of shifted Poisson processes. This rigidity result has a lot of implications in terms of joining and disjointness for the corresponding Poisson suspension. In particular, we prove that its ergodic self-joinings are Poisson joinings, which provides an analog, in the Poissonian context, of the GAG property for Gaussian dynamical systems.
Keywords
Cite
@article{arxiv.1509.07802,
title = {Poisson suspensions and Sushis},
author = {Elise Janvresse and Emmanuel Roy and Thierry De La Rue},
journal= {arXiv preprint arXiv:1509.07802},
year = {2018}
}