Electronic Communications in Probability

Coalescing random walk on unimodular graphs

Eric Foxall, Tom Hutchcroft, and Matthew Junge

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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

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

Received: 6 April 2018
Accepted: 2 May 2018
First available in Project Euclid: 13 September 2018

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Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

coalescing random walk unimodular random graph voter model

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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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