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- W1822137046 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 [Comm. Math. Phys. 121 (1989) 501–505] argument proving uniqueness of the infinite-cluster). The proof is based on the generalization of a reverse Poincaré inequality proved in Chatterjee and Sen (2013). 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 $qge1$." @default.
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- W1822137046 date "2016-09-01" @default.
- W1822137046 modified "2023-09-27" @default.
- W1822137046 title "A quantitative Burton–Keane estimate under strong FKG condition" @default.
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- W1822137046 doi "https://doi.org/10.1214/15-aop1049" @default.
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