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Collisions of random walks

Martin T. BarlowYuval PeresPerla Sousi — 2012

Annales de l'I.H.P. Probabilités et statistiques

A recurrent graph G has the infinite collision property if two independent random walks on G , started at the same point, collide infinitely often a.s. We give a simple criterion in terms of Green functions for a graph to have this property, and use it to prove that a critical Galton–Watson tree with finite variance conditioned to survive, the incipient infinite cluster in d with d 19 and the uniform spanning tree in 2 all have the infinite collision property. For power-law combs and spherically symmetric...

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