Open Access
2004 Recurrent Graphs where Two Independent Random Walks Collide Finitely Often
Manjunath Krishnapur, Yuval Peres
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Electron. Commun. Probab. 9: 72-81 (2004). DOI: 10.1214/ECP.v9-1111


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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Manjunath Krishnapur. Yuval Peres. "Recurrent Graphs where Two Independent Random Walks Collide Finitely Often." Electron. Commun. Probab. 9 72 - 81, 2004.


Accepted: 30 July 2004; Published: 2004
First available in Project Euclid: 26 May 2016

zbMATH: 1060.60044
MathSciNet: MR2081461
Digital Object Identifier: 10.1214/ECP.v9-1111

Primary: 60B99 , 60G50 , 60J10

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