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On Large Deviations for the Cover Time of Two-dimensional Torus by Comets, Francis; Gallesco, Christophe; Popov, Serguei; Vachkovskaia, Marina is a scholarly article available to read on EtoBox.

What is On Large Deviations for the Cover Time of Two-dimensional Torus about?

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.

Author

Comets, Francis; Gallesco, Christophe; Popov, Serguei; Vachkovskaia, Marina

Published

2013

Language

EN