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Brownian Bridge Asymptotics for the Subcritical Bernoulli Bond Percolation

Yevgeniy Kovchegov
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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.

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Yevgeniy Kovchegov. 2002-05-14. Brownian Bridge Asymptotics for the Subcritical Bernoulli Bond Percolation. https://arxiv.org/abs/math/0112272

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