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arXiv · 1510.04721

Site recurrence for coalescing random walk

Itai Benjamini·Eric Foxall·Ori Gurel-Gurevich·Matthew Junge·Harry Kesten
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Abstract

Begin continuous time random walks from every vertex of a graph and have particles coalesce when they collide. We use a duality relation with the voter model to prove the process is site recurrent on bounded degree graphs, and for Galton-Watson trees whose offspring distribution has exponential tail. We prove bounds on the occupation probability of a site, as well as a general 0-1 law. Similar conclusions hold for a coalescing process on trees where particles do not backtrack.

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Itai Benjamini, Eric Foxall, Ori Gurel-Gurevich, Matthew Junge, Harry Kesten. 2015-10-15. Site recurrence for coalescing random walk. https://arxiv.org/abs/1510.04721

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