Collisions of Random Walks - Mathematics > Probability

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Abstract: A recurrent graph \$G\$ has the infinite collision property if two independentrandom 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 thisproperty, and use it to prove that a critical Galton-Watson tree with finitevariance conditioned to survive, the incipient infinite cluster in \$\Z^d\$ with\$d \ge 19\$ and the uniform spanning tree in \$\Z^2\$ all have the infinitecollision property. For power-law combs and spherically symmetric trees, wedetermine precisely the phase boundary for the infinite collision property.

Autor: Martin T. Barlow, Yuval Peres, Perla Sousi

Fuente: https://arxiv.org/