Indistinguishability of Percolation Clusters
Lyons, Russell ; Schramm, Oded
arXiv, 9811170 / Harvested from arXiv
Text on arXiv
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 non-decay of connectivity (a.k.a. long-range order). We then derive applications concerning uniqueness in Kazhdan groups and in wreath products, and inequalities for $p_u$.
Publié le : 1998-11-29
Classification:  Mathematics - Probability,  Mathematical Physics,  82B43, 60B99 (Primary), 60K35, 60D05 (Secondary) 
@article{9811170,
     author = {Lyons, Russell and Schramm, Oded},
     title = {Indistinguishability of Percolation Clusters},
     journal = {arXiv},
     volume = {1998},
     number = {0},
     year = {1998},
     language = {en},
     url = {http://dml.mathdoc.fr/item/9811170}
}

Lyons, Russell; Schramm, Oded. Indistinguishability of Percolation Clusters. arXiv, Tome 1998 (1998) no. 0, . http://gdmltest.u-ga.fr/item/9811170/