Shape transition under excess self-intersections for transient random walk

Amine Asselah

Shape transition under excess self-intersections for transient random walk

Probability 2009-03-14 v3 Mathematical Physics math.MP

Authors: Amine Asselah

Abstract

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.

Keywords

random walk in random environment random walks

Cite

@article{arxiv.0804.2616,
  title  = {Shape transition under excess self-intersections for transient random walk},
  author = {Amine Asselah},
  journal= {arXiv preprint arXiv:0804.2616},
  year   = {2009}
}

Comments

35 pages. Final revised version

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