Distances in the highly supercritical percolation cluster

Anne-Laure Basdevant (1) , Nathanaël Enriquez (1, 2) , Lucas Gerin (1)

1 MODAL'X - Modélisation aléatoire de Paris X
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

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).

Mots clés: first-passage percolation; supercritical percolation; TASEP

Domaines: Probabilités [math.PR]

Anne-Laure Basdevant, Nathanaël Enriquez, Lucas Gerin. Distances in the highly supercritical percolation cluster. Annals of Probability, 2013, 41 (6), pp.4342-4358. ⟨hal-00639584v2⟩