Electronic Journal of Probability

On cover times for 2D lattices

Jian Ding

Abstract

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

Article information

Source
Electron. J. Probab., Volume 17 (2012), paper no. 45, 18 pp.

Dates
Accepted: 16 June 2012
First available in Project Euclid: 4 June 2016

https://projecteuclid.org/euclid.ejp/1465062367

Digital Object Identifier
doi:10.1214/EJP.v17-2089

Mathematical Reviews number (MathSciNet)
MR2946152

Zentralblatt MATH identifier
1258.60044

Rights

Citation

Ding, Jian. On cover times for 2D lattices. Electron. J. Probab. 17 (2012), paper no. 45, 18 pp. doi:10.1214/EJP.v17-2089. https://projecteuclid.org/euclid.ejp/1465062367

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