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arXiv · 1110.3074

Supercritical self-avoiding walks are space-filling

Hugo Duminil-Copin·Gady Kozma·Ariel Yadin
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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.

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Hugo Duminil-Copin, Gady Kozma, Ariel Yadin. 2012-09-25. Supercritical self-avoiding walks are space-filling. https://arxiv.org/abs/1110.3074

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