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

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.

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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. https://doi.org/10.1214/EJP.v18-2856

Information

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

Subjects:
Primary: 60G50
Secondary: 60G55, 82C41

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