Collisions of Random Walks in Reversible Random Graphs
Abstract
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 $\mathbb{Z}^2$.
 Publication:

arXiv eprints
 Pub Date:
 May 2015
 arXiv:
 arXiv:1505.02484
 Bibcode:
 2015arXiv150502484H
 Keywords:

 Mathematics  Probability
 EPrint:
 7 pages