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The travel time in a finite box in supercritical Bernoulli percolation

   
@article{ECP3015,
	author = {Raphaël Cerf},
	title = {The travel time in a finite box in supercritical Bernoulli percolation},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {19},
	year = {2014},
	keywords = {Bernoulli percolation; travel time},
	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.},
	pages = {no. 21, 1-9},
	issn = {1083-589X},
	doi = {10.1214/ECP.v19-3015},    
        url = {http://ecp.ejpecp.org/article/view/3015}}