Ergodicity and indistinguishability in percolation theory

Abstract : This note explores the link between the ergodicity of the cluster equivalence relation restricted to its infinite locus and the indistinguishability of infinite clusters. It is an important element of the dictionary connecting orbit equivalence and percolation theory. This paper starts with a short exposition of some standard material of these theories. Then, the classic correspondence between ergodicity and indistinguishability is presented. Finally, we introduce a notion of strong indistinguishability that corresponds to strong ergodicity, and obtain that this strong indistinguishability holds in the Bernoulli case.
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Contributor : Sébastien Martineau <>
Submitted on : Monday, May 19, 2014 - 10:50:49 AM
Last modification on : Thursday, January 11, 2018 - 6:12:31 AM
Long-term archiving on: Monday, April 10, 2017 - 11:33:39 PM


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  • HAL Id : ensl-00738628, version 2
  • ARXIV : 1210.1548


Sébastien Martineau. Ergodicity and indistinguishability in percolation theory. 2014. ⟨ensl-00738628v2⟩



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