Brownian Bridge Asymptotics for the Subcritical Bernoulli Bond Percolation
Probability
2007-05-23 v3
Abstract
For the d-dimensional model of a subcritical bond percolation (p<p_c) and a point \vec{a} in Z^d, we prove that a cluster conditioned on connecting points (0,...,0) and n\vec{a} if scaled by 1/(n|vec{a}|) along \vec{a} and by 1/sqrt{n} in the orthogonal direction converges asymptotically to Time x (d-1)-dimensional Brownian Bridge.
Keywords
Cite
@article{arxiv.math/0112272,
title = {Brownian Bridge Asymptotics for the Subcritical Bernoulli Bond Percolation},
author = {Yevgeniy Kovchegov},
journal= {arXiv preprint arXiv:math/0112272},
year = {2007}
}
Comments
18 pages, no figures, LaTeX