Open Access
2013 On large deviations for the cover time of two-dimensional torus
Francis Comets, Christophe Gallesco, Serguei Popov, Marina Vachkovskaia
Author Affiliations +
Electron. J. Probab. 18: 1-18 (2013). DOI: 10.1214/EJP.v18-2856


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.


Download Citation

Francis Comets. Christophe Gallesco. Serguei Popov. Marina Vachkovskaia. "On large deviations for the cover time of two-dimensional torus." Electron. J. Probab. 18 1 - 18, 2013.


Accepted: 6 November 2013; Published: 2013
First available in Project Euclid: 4 June 2016

zbMATH: 1294.60066
MathSciNet: MR3126579
Digital Object Identifier: 10.1214/EJP.v18-2856

Primary: 60G50
Secondary: 60G55 , 82C41

Keywords: hitting time , Simple random walk , soft local time

Vol.18 • 2013
Back to Top