## Electronic Communications in Probability

### Coalescing random walk on unimodular graphs

#### Abstract

Coalescing random walk on a unimodular random rooted graph for which the root has finite expected degree visits each site infinitely often almost surely. A corollary is that an opinion in the voter model on such graphs has infinite expected lifetime. Additionally, we deduce an adaptation of our main theorem that holds uniformly for coalescing random walk on finite random unimodular graphs with degree distribution stochastically dominated by a probability measure with finite mean.

#### Article information

Source
Electron. Commun. Probab., Volume 23 (2018), paper no. 62, 10 pp.

Dates
Accepted: 2 May 2018
First available in Project Euclid: 13 September 2018

https://projecteuclid.org/euclid.ecp/1536804170

Digital Object Identifier
doi:10.1214/18-ECP136

Zentralblatt MATH identifier
06964405

#### Citation

Foxall, Eric; Hutchcroft, Tom; Junge, Matthew. Coalescing random walk on unimodular graphs. Electron. Commun. Probab. 23 (2018), paper no. 62, 10 pp. doi:10.1214/18-ECP136. https://projecteuclid.org/euclid.ecp/1536804170

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