Size of a minimal cutset in supercritical first passage percolation - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2019

Size of a minimal cutset in supercritical first passage percolation

Marie Théret

Résumé

We consider the standard model of i.i.d. first passage percolation on Z^d given a distribution G on [0, +∞] (including +∞). We suppose that G({0}) > 1 − p_c(d), i.e., the edges of positive passage time are in the subcritical regime of percolation on Z^d. We consider a cylinder of basis an hyperrectangle of dimension d − 1 whose sides have length n and of height h(n) with h(n) negligible compared to n (i.e., h(n)/n → 0 when n goes to infinity). We study the maximal flow from the top to the bottom of this cylinder. We already know that the maximal flow renormalized by n^(d−1) converges towards the flow constant which is null in the case G({0}) > 1 − p_c (d). The study of maximal flow is associated with the study of sets of edges of minimal capacity that cut the top from the bottom of the cylinder. If we denote by ψ_n the minimal cardinal of such a set of edges, we prove here that ψ_n /n^(d−1) converges almost surely towards a constant.
Fichier principal
Vignette du fichier
Size of a minimal cutset in supercritical first passage percolation.pdf (530.4 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01726599 , version 1 (09-03-2018)
hal-01726599 , version 2 (12-04-2019)

Identifiants

Citer

Barbara Dembin, Marie Théret. Size of a minimal cutset in supercritical first passage percolation. 2019. ⟨hal-01726599v2⟩

Relations

160 Consultations
358 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More