Weak isomorphisms between Bernoulli shifts

TL;DR

This paper proves that for certain groups containing a nonabelian free subgroup, all nontrivial Bernoulli shifts are weakly isomorphic, revealing a form of universality in their structure.

Contribution

It establishes that all nontrivial Bernoulli shifts over such groups are weakly isomorphic, a new result in the understanding of Bernoulli shifts.

Findings

All nontrivial Bernoulli shifts over groups with a nonabelian free subgroup are weakly isomorphic.

The result applies to a broad class of countable groups, including free groups.

This advances the classification of Bernoulli shifts in ergodic theory.

Abstract

In this note, we prove that if G is a countable group that contains a nonabelian free subgroup then every pair of nontrivial Bernoulli shifts over G are weakly isomorphic.