Indistinguishability of Percolation Clusters By
نویسندگان
چکیده
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 Ž 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
منابع مشابه
Indistinguishability of Percolation Clusters
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, a...
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