Electronic Communications in Probability

Coalescing random walk on unimodular graphs

Eric Foxall, Tom Hutchcroft, and Matthew Junge

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1536804170

Digital Object Identifier
doi:10.1214/18-ECP136

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

Keywords
coalescing random walk unimodular random graph voter model

Rights
Creative Commons Attribution 4.0 International License.

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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