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.
"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