Workshop on Invariant Random Subgroups

Given a group with a random walk it is possible to define entropy for the random walk, but also an entropy function for stationary actions. The former is an upper bound for the latter and the realisation problem asks whether every real value between 0 and the random walk entropy is realisable as the entropy of a stationary action. Recently Hartman–Yadin have applied a construction of IRSs in discrete groups (“intersectional IRSs”) to give an affirmative answer to this problem for certain groups, by using certain actions associated to IRSs.

• Yair Hartman, Ariel Yadin, Furstenberg Entropy of Intersectional Invariant Random Subgroups, Arxiv preprint.