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October 1999 Indistinguishability of Percolation Clusters
Russell Lyons, Oded Schramm
Ann. Probab. 27(4): 1809-1836 (October 1999). DOI: 10.1214/aop/1022874816

Abstract

We show that when percolation produces infinitely many infinite clusters on a Cayley graph, one cannot distinguish the clusters from each other by any invariantly defined property. This implies that uniqueness of the infinite cluster is equivalent to nondecay of connectivity (a.k.a. long-range order). We then derive applications concerning uniqueness in Kazhdan groups and in wreath products and inequalities for $p_u$.

Citation

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Russell Lyons. Oded Schramm. "Indistinguishability of Percolation Clusters." Ann. Probab. 27 (4) 1809 - 1836, October 1999. https://doi.org/10.1214/aop/1022874816

Information

Published: October 1999
First available in Project Euclid: 31 May 2002

zbMATH: 0960.60013
MathSciNet: MR1742889
Digital Object Identifier: 10.1214/aop/1022874816

Subjects:
Primary: 60B99, 82B43
Secondary: 60D05, 60K35

Rights: Copyright © 1999 Institute of Mathematical Statistics

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Vol.27 • No. 4 • October 1999
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