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On large deviations for the cover time of two-dimensional torus

   
@article{EJP2856,
	author = {Francis Comets and Christophe Gallesco and Serguei Popov and Marina Vachkovskaia},
	title = {On large deviations for the cover time of two-dimensional torus},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {18},
	year = {2013},
	keywords = {soft local time; hitting time; simple random walk},
	abstract = {Let $\mathcal{T}_n$ be the cover time of two-dimensional discrete torus $\mathbb{Z}^2_n=\mathbb{Z}^2/n\mathbb{Z}^2$. We prove that $\mathbb{P}[\mathcal{T}_n\leq \frac{4}{\pi}\gamma n^2\ln^2 n]=\exp(-n^{2(1-\sqrt{\gamma})+o(1)})$ for $\gamma\in (0,1)$. One of the main methods used in the proofs is the decoupling of the walker's trace into independent excursions by means of soft local times.},
	pages = {no. 96, 1-18},
	issn = {1083-6489},
	doi = {10.1214/EJP.v18-2856},    
        url = {http://ejp.ejpecp.org/article/view/2856}}