Distances in the highly supercritical percolation cluster
classification
🧮 math.PR
keywords
clusterdistancespercolationsupercriticalapparentlyasymmetricasymptoticallyaxis
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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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