Site recurrence for coalescing random walk

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

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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.

Original languageAmerican English
Article number47
JournalElectronic Communications in Probability
StatePublished - 2016

Bibliographical note

Publisher Copyright:
© 2016, University of Washington. All rights reserved.


  • Interacting particle system
  • Multiple random walks
  • Random walk
  • Recurrence

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