Finite connections for supercritical Bernoulli bond percolation

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 (1.2) of finite connections for super-critical Bernoulli bond percolation on Z2. These asymptotics are based on a detailed fluctuation analysis of long finite super-critical clusters or, more precisely, of dual open (sub-critical) loops which surround such clusters