Year: 2016
Type: preprint
Abstract: Dan Rudolph showed that for an amenable group $Γ$, the generic measure-preserving action of $Γ$ on a Lebesgue space has zero entropy. Here this is extended to nonamenable groups. In fact, the proof shows that every action is a factor of a zero entropy action! This uses the strange phenomena that in the presence of nonamenability, entropy can increase under a factor map. The proof uses Seward's recent generalization of Sinai's Factor Theorem, the Gaboriau-Lyons result and my theorem that for every nonabelian free group, all Bernoulli shifts factor onto each other.
Source: arXiv (Cornell University)
Author: Bowen, Lewis
Institution: The University of Texas at Austin
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W2952820475