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 / M. Campanino; D. Ioffe; O. Louidor. - In: MARKOV PROCESSES AND RELATED FIELDS. - ISSN 1024-2953. - STAMPA. - 16:(2010), pp. 225-266.
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.File in questo prodotto:
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