Supercritical self-avoiding walks are space-filling

Details Supercritical self-avoiding walks are space-filling Supercritical self-avoiding walks are space-filling

2011-10-13

arxiv.org/abs/1110.3074v1

Mathematics

Probability

12 pages, 6 figures

Scientific paper

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.

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