Large deviations for intersection local times in critical dimension

Details Large deviations for intersection local times in critical dimension Large deviations for intersection local times in critical dimension

2008-12-09

arxiv.org/abs/0812.1639v2

Annals of Probability 2010, Vol. 38, No. 2, 927-953

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/09-AOP499 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of

Scientific paper

10.1214/09-AOP499

Let $(X_t,t\geq0)$ be a continuous time simple random walk on $\mathbb{Z}^d$ ($d\geq3$), and let $l_T(x)$ be the time spent by $(X_t,t\geq0)$ on the site $x$ up to time $T$. We prove a large deviations principle for the $q$-fold self-intersection local time $I_T=\sum_{x\in\mathbb{Z}^d}l_T(x)^q$ in the critical case $q=\frac{d}{d-2}$. When $q$ is integer, we obtain similar results for the intersection local times of $q$ independent simple random walks.

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