The travel time in a finite box in supercritical Bernoulli percolation

Raphaël Cerf (Université Paris Sud)


We consider the standard site percolation model on the three dimensional cubic lattice. Starting solely with the hypothesis that $\theta(p)>0$, we prove that, for any $\alpha>0$, there exists $\kappa>0$ such that, with probability larger than $1-1/n^\alpha$, every pair of sites inside the box $\Lambda(n)$ are joined by a path having at most $\kappa(\ln n)^2$ closed sites.

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Pages: 1-9

Publication Date: April 12, 2014

DOI: 10.1214/ECP.v19-3015


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