Weak equivalence of stationary actions and the entropy realization problem

2016/03/16 by Burton, Peter, Lupini, Martino, Tamuz, Omer
#03C98 (Secondary) #37A35 (Primary) #37A40 #Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR) #Logic (math.LO)

paper · doi:10.48550/arxiv.1603.05013

Abstract

We introduce the notion of weak containment for stationary actions of a countable group and define a natural topology on the space of weak equivalence classes. We prove that Furstenberg entropy is an invariant of weak equivalence, and moreover that it descends to a continuous function on the space of weak equivalence classes.

Related

• Ultraproducts, weak equivalence and sofic entropy
• The space of stable weak equivalence classes of measure-preserving\n actions
• Furstenberg entropy values for nonsingular actions of groups without property (T)
• Weak containment rigidity for distal actions
• Topological weak containment