HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
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