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A quantitative Burton-Keane estimate under strong FKG condition | | Hugo Duminil-Copin
; Dmitry Ioffe
; Yvan Velenik
; | | Date: |
24 Sep 2014 | | Abstract: | We consider translationally-invariant percolation models on $mathbb Z^d$
satisfying the finite energy and the FKG properties. We provide explicit upper
bounds on the probability of having two distinct clusters going from the
endpoints of an edge to distance $n$ (this corresponds to a finite size version
of the celebrated Burton-Keane argument proving uniqueness of the
infinite-cluster). The proof is based on the generalization of a reverse
Poincar’e inequality proved by Chatterjee and Sen. As a consequence, we obtain
upper bounds on the probability of the so-called four-arm event for planar
random-cluster models with cluster-weight $qge 1$. | | Source: | arXiv, 1409.5199 | | Services: | Forum | Review | PDF | Favorites | |
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