Approximations of standard equivalence relations and Bernoulli percolation at pu

Damien Gaboriau; Robin Tucker-Drob

doi:10.1016/j.crma.2016.09.011

Dynamical systems/Probability theory

Approximations of standard equivalence relations and Bernoulli percolation at p_u

Presented by: Étienne Ghys

Damien Gaboriau ¹; Robin Tucker-Drob ²

¹ CNRS, Unité de mathématiques pures et appliquées, ENS-Lyon, Université de Lyon, France
² Department of Mathematics, Texas A&M University, College Station, TX, USA

Comptes Rendus. Mathématique, Volume 354 (2016) no. 11, pp. 1114-1118.

Abstract
Résumé

The goal of this note is to announce certain results in orbit equivalence theory, especially concerning the approximation of p.m.p. standard equivalence relations by increasing sequences of sub-relations, with application to the behavior of the Bernoulli percolation on Cayley graphs at the threshold $p_{u}$ .

Le but de cette note est d'annoncer certains résultats d'équivalence orbitale, concernant notamment la notion d'approximation de relations d'équivalence standard préservant la mesure de probabilité par suites croissantes de sous-relations, avec application au comportement en $p_{u}$ de la percolation de Bernoulli sur les graphes de Cayley.

Received: 2015-07-06
Accepted: 2016-09-27
Published online: 2016-10-18

DOI: 10.1016/j.crma.2016.09.011

Author's affiliations:

Damien Gaboriau ¹; Robin Tucker-Drob ²

¹ CNRS, Unité de mathématiques pures et appliquées, ENS-Lyon, Université de Lyon, France
² Department of Mathematics, Texas A&M University, College Station, TX, USA

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     author = {Damien Gaboriau and Robin Tucker-Drob},
     title = {Approximations of standard equivalence relations and {Bernoulli} percolation at \protect\emph{p}\protect\textsubscript{\protect\emph{u}}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1114--1118},
     publisher = {Elsevier},
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     year = {2016},
     doi = {10.1016/j.crma.2016.09.011},
     language = {en},
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Damien Gaboriau; Robin Tucker-Drob. Approximations of standard equivalence relations and Bernoulli percolation at p_u. Comptes Rendus. Mathématique, Volume 354 (2016) no. 11, pp. 1114-1118. doi : 10.1016/j.crma.2016.09.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.09.011/

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