%0 Journal Article
%T Shape transition under excess self-intersections for transient random walk
%A Amine Asselah
%J Mathematics
%D 2008
%I arXiv
%X We reveal a shape transition for a transient simple random walk forced to realize an excess $q$-norm of the local times, as the parameter $q$ crosses the value $q_c(d)=\frac{d}{d-2}$. Also, as an application of our approach, we establish a central limit theorem for the $q$-norm of the local times in dimension 4 or more.
%U http://arxiv.org/abs/0804.2616v3