Shape transition under excess self-intersections for transient random walk

Details Shape transition under excess self-intersections for transient random walk Shape transition under excess self-intersections for transient random walk

2008-04-16

arxiv.org/abs/0804.2616v3

Mathematics

Probability

35 pages. Final revised version

Scientific paper

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.

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