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Coalescing random walk on unimodular graphs

Probability 2018-04-06 v3

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.

Keywords

Cite

@article{arxiv.1701.02653,
  title  = {Coalescing random walk on unimodular graphs},
  author = {Eric Foxall and Tom Hutchcroft and Matthew Junge},
  journal= {arXiv preprint arXiv:1701.02653},
  year   = {2018}
}

Comments

Corrected an error in the previous argument and added two new corollaries

R2 v1 2026-06-22T17:46:18.510Z