# Recurrent Graphs where Two Independent Random Walks Collide Finitely Often

```@article{Krishnapur2004RecurrentGW,
title={Recurrent Graphs where Two Independent Random Walks Collide Finitely Often},
author={Manjunath Krishnapur and Yuval Peres},
journal={Electronic Communications in Probability},
year={2004},
volume={9},
pages={72-81}
}```
• Published 23 June 2004
• Mathematics
• Electronic Communications in Probability
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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