Poisson suspensions and infinite ergodic theory

TL;DR

This paper explores the ergodic theory of Poisson suspensions, establishing links between finite and infinite measure systems and offering new insights into their mixing, spectral properties, and relations to Gaussian systems.

Contribution

It introduces Poisson suspensions as a novel approach to infinite measure ergodic theory, analyzing their mixing, spectral, and joining properties.

Findings

Poisson suspensions connect finite and infinite ergodic theory.

They exhibit specific mixing and spectral behaviors.

Comparison with Gaussian systems reveals notable similarities and differences.

Abstract

We investigate ergodic theory of Poisson suspensions. In the process, we establish close connections between finite and infinite measure preserving ergodic theory. Poisson suspensions thus provide a new approach to infinite measure preserving ergodic theory. Fields investigated here are mixing properties, spectral theory, joinings. We also compare Poisson suspensions to the apparently similar looking Gaussian dynamical systems.