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arXiv · 1111.2302

Distances in the highly supercritical percolation cluster

Anne-Laure Basdevant·Nathanaël Enriquez·Lucas Gerin
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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+(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).

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Anne-Laure Basdevant, Nathanaël Enriquez, Lucas Gerin. 2012-10-01. Distances in the highly supercritical percolation cluster. https://arxiv.org/abs/1111.2302

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