Open Access
2018 Coalescing random walk on unimodular graphs
Eric Foxall, Tom Hutchcroft, Matthew Junge
Electron. Commun. Probab. 23: 1-10 (2018). DOI: 10.1214/18-ECP136


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.


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Eric Foxall. Tom Hutchcroft. Matthew Junge. "Coalescing random walk on unimodular graphs." Electron. Commun. Probab. 23 1 - 10, 2018.


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

zbMATH: 06964405
MathSciNet: MR3863918
Digital Object Identifier: 10.1214/18-ECP136

Primary: 60K35

Keywords: coalescing random walk , unimodular random graph , voter model

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