Recurrent graphs where two independent random walks collide finitely often

Details Recurrent graphs where two independent random walks collide finitely often Recurrent graphs where two independent random walks collide finitely often

2004-06-23

arxiv.org/abs/math/0406487v2

Mathematics

Probability

10 pages, 1 figure; Minor changes made

Scientific paper

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.

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