Size of a minimal cutset in supercritical first passage percolation

Abstract : 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.
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Contributeur : Barbara Dembin <>
Soumis le : vendredi 9 mars 2018 - 17:17:43
Dernière modification le : mardi 19 mars 2019 - 01:23:27
Document(s) archivé(s) le : dimanche 10 juin 2018 - 12:57:05


Size of a minimal cutset in su...
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  • HAL Id : hal-01726599, version 1
  • ARXIV : 1803.04272


Barbara Dembin, Marie Théret. Size of a minimal cutset in supercritical first passage percolation . 2018. 〈hal-01726599〉



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