%0 Journal Article
%T Large deviations estimates for self-intersection local times for simple random walk in $\Z^3$
%A Amine Asselah
%J Mathematics
%D 2006
%I arXiv
%X We obtain large deviations estimates for the self-intersection local times for a symmetric random walk in dimension 3. Also, we show that the main contribution to making the self-intersection large, in a time period of length $n$, comes from sites visited less than some power of $\log(n)$. This is opposite to the situation in dimensions larger or equal to 5. Finally, we present two applications of our estimates: (i) to moderate deviations estimates for the range of a random walk, and (ii) to moderate deviations for random walk in random sceneries.
%U http://arxiv.org/abs/math/0602074v1