Brownian Bridge Asymptotics for the Subcritical Bernoulli Bond Percolation
Abstract
For the d-dimensional model of a subcritical bond percolation (p<pc) and a point a in Zd, we prove that a cluster conditioned on connecting points (0,...,0) and na if scaled by 1/(n|veca|) along a and by 1/sqrtn in the orthogonal direction converges asymptotically to Time x (d-1)-dimensional Brownian Bridge.
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