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Recurrent Graphs where Two Independent Random Walks Collide Finitely Often
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Manjunath Krishnapur, University of California at Berkeley, USA
Yuval Peres, University of California at Berkeley, USA
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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 $Z^2$.
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Full text: PDF
Pages: 72-81
Published on: July 30, 2004
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Electronic Communications in Probability. ISSN: 1083-589X |
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