Open Access
2015 Collisions of random walks in reversible random graphs
Tom Hutchcroft, Yuval Peres
Author Affiliations +
Electron. Commun. Probab. 20: 1-6 (2015). DOI: 10.1214/ECP.v20-4330


We prove that in any recurrent reversible random rooted graph, two independent simple random walks started at the same vertex collide infinitely often almost surely. This applies to the Uniform Infinite Planar Triangulation and Quadrangulation and to the Incipient Infinite Cluster in $\mathbb{Z}^2$.


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Tom Hutchcroft. Yuval Peres. "Collisions of random walks in reversible random graphs." Electron. Commun. Probab. 20 1 - 6, 2015.


Accepted: 15 September 2015; Published: 2015
First available in Project Euclid: 7 June 2016

zbMATH: 1329.60357
MathSciNet: MR3399814
Digital Object Identifier: 10.1214/ECP.v20-4330

Primary: 60J10
Secondary: 05C81 , 60K37

Keywords: Collisions , Random walks , unimodular random graphs

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