On cover times for 2D lattices

Details On cover times for 2D lattices On cover times for 2D lattices

2011-10-15

arxiv.org/abs/1110.3367v1

Mathematics

Probability

18 pages

Scientific paper

We study the cover time by (continuous-time) random walk on the 2D box of side length $n$ with wired boundary or unwired boundary, and show that in both cases with probability approaching 1 as $n$ increases, $\sqrt{\tau_{\mathrm{cov}}}=\sqrt{2n^2}[\sqrt{2/\pi} \log n + O(\log\log n)]$. Our result also extends to the random walk on 2D torus. This improves a result of Dembo, Peres, Rosen, and Zeitouni (2004) and makes progress towards a conjecture of Bramson and Zeitouni (2009).

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