Recurrent graphs where two independent random walks collide finitely often
Probability
2007-05-23 v2
Abstract
We present a class of graphs where simple random walk is recurrent, yet two independent walkers meet only finitely many times almost surely. In particular, the comb lattice, obtained from Z^2 by removing all horizontal edges off the X-axis, has this property. We also conjecture that the same property holds for some other graphs, including the incipient infinite cluster for critical percolation in Z^2.
Cite
@article{arxiv.math/0406487,
title = {Recurrent graphs where two independent random walks collide finitely often},
author = {Manjunath Krishnapur and Yuval Peres},
journal= {arXiv preprint arXiv:math/0406487},
year = {2007}
}
Comments
10 pages, 1 figure; Minor changes made