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Recurrent graphs where two independent random walks collide finitely often. (English) Zbl 1060.60044
Summary: 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 \(\mathbb Z^2\) 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 \(\mathbb Z^2\).

MSC:
60G50 Sums of independent random variables; random walks
60C05 Combinatorial probability
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
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