Ergodicity and indistinguishability in percolation theory

Abstract : This paper explores the link between the ergodicity of the clus-ter equivalence relation restricted to its infinite locus and the indis-tinguishability of infinite clusters. It is an important element of the dictionary connecting orbit equivalence and percolation theory. This note starts with a short exposition of some standard material of these theories. Then, the classic correspondence between ergodicity and in-distinguishability 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. We also define an invariant percolation that is not insertion-tolerant, sat-isfies the Indistinguishability Property and does not satisfy the Strong Indistinguishability Property.
Type de document :
Pré-publication, Document de travail
2014
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https://hal-ens-lyon.archives-ouvertes.fr/ensl-00738628
Contributeur : Sébastien Martineau <>
Soumis le : lundi 27 octobre 2014 - 16:44:28
Dernière modification le : jeudi 11 janvier 2018 - 06:12:31
Document(s) archivé(s) le : mercredi 28 janvier 2015 - 11:51:42

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Indistinguishability.pdf
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  • HAL Id : ensl-00738628, version 3
  • ARXIV : 1210.1548

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Sébastien Martineau. Ergodicity and indistinguishability in percolation theory. 2014. 〈ensl-00738628v3〉

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