| Título: | Large deviations for self-intersection local times in subcritical dimensions |
| Autores: | Laurent, Clément; Université de Provence |
| Fecha: | 2012-01-01 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: | Peer-reviewed Article |
| Tema: |
Large deviations; intersection local times; self-intersection. 60F10; 60G50; 60J27; 60J55 |
| Descripción: | Let $(X_t,t\geq 0)$ be a simple symmetric random walk on $\mathbb{Z}^d$ and for any $x\in\mathbb{Z}^d$, let $ l_t(x)$ be its local time at site $x$. For any $p>1$, we denote by$ I_t= \sum\limits_{x\in\mathbb{Z}^d} l_t(x)^p $ the p-fold self-intersection local times (SILT). Becker and König recently proved a large deviations principle for $I_t$ for all $p>1$ such that $p(d-2/p)<2$. We extend these results to a broader scale of deviations and to the whole subcritical domain $p(d-2)<d$. Moreover, we unify the proofs of the large deviations principle using a method introduced by Castell for the critical case $p(d-2)=d$. |
| Idioma: | Inglés |
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