Title: The Poisson Suspension in Probability and Ergodic Theory


Abstract: One can naturally associate with every infinite measure space a Poisson point process. Through this construction, a group of measure-preserving transformations of the underlying space is associated a group of probability-preserving transformations of the associated Poisson point process. This construction is known as Poisson suspension.In the first part of the talk, I will introduce Poisson suspensions and use them to study stationary Infinitely Divisible processes indexed by a general Polish group. This perspective provides a general characterization of the ergodicity of such processes that goes beyond conventional assumptions about the indexing group (such as Abelian, amenable, locally compact).
In the second part of the talk, I will discuss fundamental properties of Poisson suspensions of Polish groups, and in particular descriptive set theoretic aspects with regard to the question whether pointwise ("spatial") actions admit pointwise Poisson suspensions.
The main results that will be introduced are joint work with Emmanuel Roy.

Live broadcast and recording link: https://huji.cloud.panopto.eu/Panopto/Pages/Viewer.aspx?id=d9741536-4ff6-4e46-8810-affc00e58c28