**Papers Published**

- Foxall, E; Hutchcroft, T; Junge, M,
*Coalescing random walk on unimodular graphs*, Electronic Communications in Probability, vol. 23 (January, 2018), Institute of Mathematical Statistics

(last updated on 2019/05/23)**Abstract:**

© 2018, University of Washington. All rights reserved. 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.