Distances in the highly supercritical percolation cluster

Details Distances in the highly supercritical percolation cluster Distances in the highly supercritical percolation cluster

2011-11-09

arxiv.org/abs/1111.2302v1

Mathematics

Probability

15 pages

Scientific paper

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 a
apparently new connection with the TASEP (totally asymmetric simple exclusion
process).

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