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2014 The travel time in a finite box in supercritical Bernoulli percolation
Raphaël Cerf
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Electron. Commun. Probab. 19: 1-9 (2014). DOI: 10.1214/ECP.v19-3015

Abstract

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.

Citation

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Raphaël Cerf. "The travel time in a finite box in supercritical Bernoulli percolation." Electron. Commun. Probab. 19 1 - 9, 2014. https://doi.org/10.1214/ECP.v19-3015

Information

Accepted: 12 April 2014; Published: 2014
First available in Project Euclid: 7 June 2016

zbMATH: 1312.60115
MathSciNet: MR3197117
Digital Object Identifier: 10.1214/ECP.v19-3015

Subjects:
Primary: 60K35
Secondary: 82B43

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