Poisson suspensions and Sushis

Elise Janvresse (1) , Emmanuel Roy (2) , Thierry de La Rue (3)

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352
2 LAGA - Laboratoire Analyse, Géométrie et Applications
3 LMRS - Laboratoire de Mathématiques Raphaël Salem

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.

Mots clés: Point process; Poisson suspension; joinings

Domaines: Probabilités [math.PR]; Systèmes dynamiques [math.DS]

Elise Janvresse, Emmanuel Roy, Thierry de La Rue. Poisson suspensions and Sushis. 2017. ⟨hal-01205239v3⟩