Recurrent graphs where two independent random walks collide finitely often
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 Xaxis, 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 2004
 arXiv:
 arXiv:math/0406487
 Bibcode:
 2004math......6487K
 Keywords:

 Mathematics  Probability
 EPrint:
 10 pages, 1 figure