%0 Journal Article %T Large deviations for intersection local times in critical dimension %A Fabienne Castell %J Mathematics %D 2008 %I arXiv %R 10.1214/09-AOP499 %X 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. %U http://arxiv.org/abs/0812.1639v2