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On cover times for 2D lattices


 
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1. Title Title of document On cover times for 2D lattices
 
2. Creator Author's name, affiliation, country Jian Ding; Stanford University; United States
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Cover times ; Gaussian free fields ; random walks
 
3. Subject Subject classification 60J10; 60G60; 60G15
 
4. Description 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,$\sqrt{\tau_{\mathrm{cov}}}=\sqrt{2n^2 [\sqrt{2/\pi} \log n + O(\log\log n)]$. This improves a result of Dembo, Peres, Rosen, and Zeitouni (2004) and makes progresstowards a conjecture of Bramson and Zeitouni (2009).
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) Microsoft Research
 
7. Date (YYYY-MM-DD) 2012-06-16
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/2089
 
10. Identifier Digital Object Identifier 10.1214/EJP.v17-2089
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 17
 
12. Language English=en en
 
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