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On cover times for 2D lattices

   
@article{EJP2089,
	author = {Jian Ding},
	title = {On cover times for 2D lattices},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {17},
	year = {2012},
	keywords = {Cover times ; Gaussian free fields ; random walks},
	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).},
	pages = {no. 45, 1-18},
	issn = {1083-6489},
	doi = {10.1214/EJP.v17-2089},    
        url = {http://ejp.ejpecp.org/article/view/2089}}