Two vertices x and y are said to be finitely connected if they belong to the same cluster and this cluster is finite. We derive sharp asymptotics of finite connections for super-critical Bernoulli bond percolation on Z^2. These asymptotics are based on a detailed fluctuation analysis of long finite super-critical clusters or, more precisely, of dual open (sub-critical) loopswhich surround such clusters.

Finite Connections for Supercritical Bernoulli Bond Percolation in 2D

CAMPANINO, MASSIMO;
2010

Abstract

Two vertices x and y are said to be finitely connected if they belong to the same cluster and this cluster is finite. We derive sharp asymptotics of finite connections for super-critical Bernoulli bond percolation on Z^2. These asymptotics are based on a detailed fluctuation analysis of long finite super-critical clusters or, more precisely, of dual open (sub-critical) loopswhich surround such clusters.
M. Campanino; D. Ioffe; O. Louidor
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/90439
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