Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 23 (2018), paper no. 62, 10 pp.
Coalescing random walk on unimodular graphs
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.
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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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