Entropy, orbit equivalence, and sparse connectivity

Abstract: It was shown a few years ago by Tim Austin that if an orbit equivalence between probability-measure-preserving actions of finitely generated amenable groups is integrable then it preserves entropy. I will discuss some joint work with Hanfeng Li in which we show that the same conclusion holds for the maximal sofic entropy when the acting groups are countable and sofic and contain an amenable w-normal subgroup which is not locally virtually cyclic, and that it is moreover enough to assume that the Shannon entropy of the cocycle partitions is finite (what we call Shannon orbit equivalence). One consequence is that two Bernoulli actions of a group in the above class are Shannon orbit equivalent if and only if they are conjugate.

algebraic topologyfunctional analysisgroup theorygeometric topologyoperator algebras

Audience: researchers in the topic

Vienna Geometry and Analysis on Groups Seminar