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2012 On cover times for 2D lattices
Jian Ding
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Electron. J. Probab. 17: 1-18 (2012). DOI: 10.1214/EJP.v17-2089

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).

Citation

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Jian Ding. "On cover times for 2D lattices." Electron. J. Probab. 17 1 - 18, 2012. https://doi.org/10.1214/EJP.v17-2089

Information

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

zbMATH: 1258.60044
MathSciNet: MR2946152
Digital Object Identifier: 10.1214/EJP.v17-2089

Subjects:
Primary: 60J10
Secondary: 60G15 , 60G60

Keywords: Cover times , Gaussian free fields , Random walks

JOURNAL ARTICLE
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Vol.17 • 2012
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