Brownian Bridge Asymptotics for the Subcritical Bernoulli Bond Percolation

Details Brownian Bridge Asymptotics for the Subcritical Bernoulli Bond Percolation Brownian Bridge Asymptotics for the Subcritical Bernoulli Bond Percolation

2001-12-24

arxiv.org/abs/math/0112272v3

Mathematics

Probability

18 pages, no figures, LaTeX

Scientific paper

For the d-dimensional model of a subcritical bond percolation (ppoint \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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