Supercritical self-avoiding walks are space-filling

Hugo Duminil-Copin; Gady Kozma; Ariel Yadin

Annales de l'I.H.P. Probabilités et statistiques (2014)

  • Volume: 50, Issue: 2, page 315-326
  • ISSN: 0246-0203

Abstract

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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 d is proportional to μ - length ( γ ) . When μ is supercritical (i.e. μ l t ; 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.

How to cite

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Duminil-Copin, Hugo, Kozma, Gady, and Yadin, Ariel. "Supercritical self-avoiding walks are space-filling." Annales de l'I.H.P. Probabilités et statistiques 50.2 (2014): 315-326. <http://eudml.org/doc/272072>.

@article{Duminil2014,
abstract = {In this article, we consider the following model of self-avoiding walk: the probability of a self-avoiding trajectory $\gamma $ between two points on the boundary of a finite subdomain of $\mathbb \{Z\}^\{d\}$ is proportional to $\mu ^\{-\mbox\{length\}(\gamma )\}$. When $\mu $ is supercritical (i.e. $\mu &lt;\mu _\{c\}$ where $\mu _\{c\}$ is the connective constant of the lattice), we show that the random trajectory becomes space-filling when taking the scaling limit.},
author = {Duminil-Copin, Hugo, Kozma, Gady, Yadin, Ariel},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {self avoiding walk; connective constant},
language = {eng},
number = {2},
pages = {315-326},
publisher = {Gauthier-Villars},
title = {Supercritical self-avoiding walks are space-filling},
url = {http://eudml.org/doc/272072},
volume = {50},
year = {2014},
}

TY - JOUR
AU - Duminil-Copin, Hugo
AU - Kozma, Gady
AU - Yadin, Ariel
TI - Supercritical self-avoiding walks are space-filling
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2014
PB - Gauthier-Villars
VL - 50
IS - 2
SP - 315
EP - 326
AB - In this article, we consider the following model of self-avoiding walk: the probability of a self-avoiding trajectory $\gamma $ between two points on the boundary of a finite subdomain of $\mathbb {Z}^{d}$ is proportional to $\mu ^{-\mbox{length}(\gamma )}$. When $\mu $ is supercritical (i.e. $\mu &lt;\mu _{c}$ where $\mu _{c}$ is the connective constant of the lattice), we show that the random trajectory becomes space-filling when taking the scaling limit.
LA - eng
KW - self avoiding walk; connective constant
UR - http://eudml.org/doc/272072
ER -

References

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