## Electronic Communications in Probability

### Site recurrence for coalescing random walk

#### 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.

#### Article information

Source
Electron. Commun. Probab., Volume 21 (2016), paper no. 47, 12 pp.

Dates
Accepted: 10 June 2016
First available in Project Euclid: 20 June 2016

https://projecteuclid.org/euclid.ecp/1466450523

Digital Object Identifier
doi:10.1214/16-ECP5

Mathematical Reviews number (MathSciNet)
MR3522593

Zentralblatt MATH identifier
1345.60110

Subjects
Primary: 60J27: Continuous-time Markov processes on discrete state spaces

#### Citation

Benjamini, Itai; Foxall, Eric; Gurel-Gurevich, Ori; Junge, Matthew; Kesten, Harry. Site recurrence for coalescing random walk. Electron. Commun. Probab. 21 (2016), paper no. 47, 12 pp. doi:10.1214/16-ECP5. https://projecteuclid.org/euclid.ecp/1466450523

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