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Coalescing random walk on unimodular graphs

Foxall, Eric and Hutchcroft, Tom and Junge, Matthew (2018) Coalescing random walk on unimodular graphs. Electronic Communications in Probability, 23 . Art. No. 62. ISSN 1083-589X. doi:10.1214/18-ecp136. https://resolver.caltech.edu/CaltechAUTHORS:20210923-184021815

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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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1214/18-ecp136DOIArticle
https://arxiv.org/abs/1701.02653arXivDiscussion Paper
ORCID:
AuthorORCID
Hutchcroft, Tom0000-0003-0061-593X
Alternate Title:Site recurrence for coalescing random walk on unimodular graphs
Additional Information:© 2018 The Author(s). Creative Commons Attribution 4.0 International License. Received: 6 April 2018; Accepted: 2 May 2018; Published: 2018. First available in Project Euclid: 13 September 2018.
Subject Keywords:coalescing random walk, unimodular random graph, voter model
Classification Code:AMS MSC 2010: 60K35
DOI:10.1214/18-ecp136
Record Number:CaltechAUTHORS:20210923-184021815
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210923-184021815
Official Citation:Eric Foxall. Tom Hutchcroft. Matthew Junge. "Coalescing random walk on unimodular graphs." Electron. Commun. Probab. 23 1 - 10, 2018. https://doi.org/10.1214/18-ECP136
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:111019
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:23 Sep 2021 21:21
Last Modified:23 Sep 2021 21:22

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