Supercritical self-avoiding walks are space-filling
Probability
2012-09-26 v3 Mathematical Physics
Combinatorics
math.MP
Abstract
We consider random self-avoiding walks between two points on the boundary of a finite subdomain of Z^d (the probability of a self-avoiding trajectory gamma is proportional to mu^{-length(gamma)}). We show that the random trajectory becomes space-filling in the scaling limit when the parameter mu is supercritical.
Cite
@article{arxiv.1110.3074,
title = {Supercritical self-avoiding walks are space-filling},
author = {Hugo Duminil-Copin and Gady Kozma and Ariel Yadin},
journal= {arXiv preprint arXiv:1110.3074},
year = {2012}
}
Comments
12 pages, 6 figures