Abstract
On the supercritical percolation cluster with parameter $p$, the distances between two distant points of the axis are asymptotically increased by a factor $1+\frac{1-p}{2}+o(1-p)$ with respect to the usual distance. The proof is based on an apparently new connection with the TASEP (totally asymmetric simple exclusion process).
Citation
Anne-Laure Basdevant. Nathanaël Enriquez. Lucas Gerin. "Distances in the highly supercritical percolation cluster." Ann. Probab. 41 (6) 4342 - 4358, November 2013. https://doi.org/10.1214/12-AOP802
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