Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

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.
Document type :
Preprints, Working Papers, ...
Complete list of metadata
Contributor : Sébastien Martineau Connect in order to contact the contributor
Submitted on : Monday, October 27, 2014 - 4:44:28 PM
Last modification on : Wednesday, November 20, 2019 - 7:28:38 AM
Long-term archiving on: : Wednesday, January 28, 2015 - 11:51:42 AM


Files produced by the author(s)


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



Sébastien Martineau. Ergodicity and indistinguishability in percolation theory. 2014. ⟨ensl-00738628v3⟩



Record views


Files downloads