Supercritical self-avoiding walks are space-filling
Annales de l'I.H.P. Probabilités et statistiques, Volume 50 (2014) no. 2, p. 315-326

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<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.

Dans cet article, nous considérons le modèle suivant de marches auto-évitantes : la probabilité d’une trajectoire auto-évitante γ entre deux points fixés d’un sous-domaine fini de d est proportionnelle à μ -length(γ) . Lorsque le paramètre μ est supercritique (i.e. μ<μ c ou μ c est la constante de connectivité du réseau), nous prouvons que la trajectoire aléatoire remplit l’espace lorsque l’on considère la limite d’échelle du modèle.

DOI : https://doi.org/10.1214/12-AIHP528
Classification:  60K35,  60C05,  82C41
Keywords: self avoiding walk, connective constant
@article{AIHPB_2014__50_2_315_0,
     author = {Duminil-Copin, Hugo and Kozma, Gady and Yadin, Ariel},
     title = {Supercritical self-avoiding walks are space-filling},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {50},
     number = {2},
     year = {2014},
     pages = {315-326},
     doi = {10.1214/12-AIHP528},
     zbl = {1292.60096},
     mrnumber = {3189073},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2014__50_2_315_0}
}
Duminil-Copin, Hugo; Kozma, Gady; Yadin, Ariel. Supercritical self-avoiding walks are space-filling. Annales de l'I.H.P. Probabilités et statistiques, Volume 50 (2014) no. 2, pp. 315-326. doi : 10.1214/12-AIHP528. http://www.numdam.org/item/AIHPB_2014__50_2_315_0/

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