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 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.
- Publication:
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arXiv Mathematics e-prints
- Pub Date:
- June 2004
- DOI:
- 10.48550/arXiv.math/0406487
- arXiv:
- arXiv:math/0406487
- Bibcode:
- 2004math......6487K
- Keywords:
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- Mathematics - Probability
- E-Print:
- 10 pages, 1 figure