Open Access
2016 Site recurrence for coalescing random walk
Itai Benjamini, Eric Foxall, Ori Gurel-Gurevich, Matthew Junge, Harry Kesten
Electron. Commun. Probab. 21: 1-12 (2016). DOI: 10.1214/16-ECP5


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. "Site recurrence for coalescing random walk." Electron. Commun. Probab. 21 1 - 12, 2016.


Received: 31 January 2016; Accepted: 10 June 2016; Published: 2016
First available in Project Euclid: 20 June 2016

zbMATH: 1345.60110
MathSciNet: MR3522593
Digital Object Identifier: 10.1214/16-ECP5

Primary: 60J27

Keywords: Interacting particle system , multiple random walks , Random walk , recurrence

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