The orbital equivalence of Bernoulli actions and their Sinai factors

Zemer Kosloff; Terry Soo

doi:10.3934/jmd.2021005

Article Contents

2021, Volume 17: 145-182. Doi: 10.3934/jmd.2021005

This volume Previous Article Local rigidity of certain actions of solvable groups on the boundaries of rank-one symmetric spaces Next Article Cusp excursion in hyperbolic manifolds and singularity of harmonic measure

The orbital equivalence of Bernoulli actions and their Sinai factors

Zemer Kosloff^1, and
Terry Soo^2,

1.
Einstein Institute of Mathematics, Hebrew University of Jerusalem, Edmund J. Safra Campus, Givat Ram. Jerusalem, 9190401, Israel
2.
Department of Statistical Science, University College London, Gower Street, London WC1E 6BT, United Kingdom

ZK: Funded in part by ISF grant No. 1570/17.

Received: May 07, 2020

Revised: December 28, 2020

Published: March 2021

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Abstract

Given a countable amenable group $ G $ and $ \lambda \in (0,1) $, we give an elementary construction of a type-Ⅲ$ _{\lambda} $ Bernoulli group action. In the case where $ G $ is the integers, we show that our nonsingular Bernoulli shifts have independent and identically distributed factors.

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Mathematics Subject Classification: Primary: 37A40, 37A20; Secondary: 37A35, 60G09.

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