Recurrent graphs where two independent random walks collide finitely often

2004/06/23 by Manjunath Krishnapur, Yuval Peres, Krishnapur, Manjunath +1 · 1 citation
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.math/0406487

10 pages, 1 figure; Minor changes made

arxiv created 2004/08/02 · arxiv updated 2009/12/01

Abstract

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 Z² 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 Z².

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• Collisions of random walks on comb graphs with a planar base

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