Supercritical self-avoiding walks are space-filling

Hugo Duminil-Copin; Gady Kozma; Ariel Yadin

doi:10.1214/12-AIHP528

Supercritical self-avoiding walks are space-filling

Hugo Duminil-Copin, Gady Kozma, Ariel Yadin

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

In this article, we consider the following model of self-avoiding walk: the probability of a self-avoiding trajectory γ between two points on the boundary of a finite subdomain of ℤ is proportional to μ ^-length (γ). When μ is supercritical (i.e. μ < μ_c where μ_c is the connective constant of the lattice), we show that the random trajectory becomes space-filling when taking the scaling limit.

Original language	English
Pages (from-to)	315-326
Number of pages	12
Journal	Annales de l'institut Henri Poincare (B) Probability and Statistics
Volume	50
Issue number	2
DOIs	https://doi.org/10.1214/12-AIHP528
State	Published - 1 Jan 2014

Keywords

Connective constant
Self avoiding walk

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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Supercritical self-avoiding walks are space-filling

Abstract

Keywords

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