Analysis and Probability seminar

Abstract: It is known for a long time, due to a celebrated theorem of Ornstein and Weiss, that (classical/plain) orbit equivalence offers no information about ergodic probability measure preserving actions of amenable groups. On the other hand, conjugacy is too intractable—and effectively almost hopeless to study in any generality. Quantitative orbit equivalence aims to bridge this gap by adding intermediate layers of rigidity—a strategy that has borne fruit already in the late 1960s, but was used as a general framework only semi-recently. In this talk, I will introduce aspects of quantitative orbit equivalence and present a complete picture of it for integer odometers. This is joint work with Petr Naryshkin.