| Título: | On large deviations for the cover time of two-dimensional torus |
| Autores: |
Comets, Francis; Université Paris-7 Gallesco, Christophe; UNICAMP Popov, Serguei; UNICAMP Vachkovskaia, Marina; UNICAMP |
| Fecha: | 2013-01-04 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: | Peer-reviewed Article |
| Tema: |
soft local time; hitting time; simple random walk 60G50; 82C41; 60G55 |
| Descripción: | 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. |
| Idioma: | Inglés |
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