Recurrent graphs where two independent random walks collide finitely often

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We present a class of graphs where simple random walk is recurrent, yet two independent walkers meet only finitely many times almost surely. In particular, the comb lattice, obtained from Z^2 by removing all horizontal edges off the X-axis, has this property. We also conjecture that the same property holds for some other graphs, including the incipient infinite cluster for critical percolation in Z^2.
10 pages, 1 figure; Minor changes made

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Probability

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http://salesiana.dossiersoluciones.com/handle/123456789/71659

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0406487
 http://arxiv.org/abs/math/0406487

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arXiv