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Published September 2015 | Submitted + Published
Journal Article Open

Collisions of random walks in reversible random graphs


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 Z².

Additional Information

© 2015 The Author(s). Creative Commons Attribution 3.0 License. Submitted to ECP on May 26, 2015, final version accepted on September 15, 2015. First available in Project Euclid: 7 June 2016. This work was carried out while TH was an intern at Microsoft Research. We thank Itai Benjamini for suggesting this problem, and also thank Lewis Bowen, Perla Sousi and Omer Tamuz for helpful discussions.

Attached Files

Published - ECP.v20-4330.pdf

Submitted - 1505.02484.pdf


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