Existence and continuity of the flow constant in first passage percolation

Abstract : We consider the model of i.i.d. first passage percolation on Z^d , where we associate with the edges of the graph a family of i.i.d. random variables with common distribution G on [0, +∞] (including +∞). Whereas the time constant is associated to the study of 1-dimensional paths with minimal weight, namely geodesics, the flow constant is associated to the study of (d−1)-dimensional surfaces with minimal weight. In this article, we investigate the existence of the flow constant under the only hypothesis that G({+∞}) < p c (d) (in particular without any moment assumption), the convergence of some natural maximal flows towards this constant, and the continuity of this constant with regard to the distribution G.
Type de document :
Pré-publication, Document de travail
IF_PREPUB. 2017
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https://hal.archives-ouvertes.fr/hal-01568243
Contributeur : Raphaël Rossignol <>
Soumis le : mardi 25 juillet 2017 - 05:55:29
Dernière modification le : samedi 29 juillet 2017 - 01:10:24

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cont_flux.pdf
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  • HAL Id : hal-01568243, version 1
  • ARXIV : 1707.08766

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INSMI | PMA | UPMC | USPC

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Raphaël Rossignol, Marie Théret. Existence and continuity of the flow constant in first passage percolation. IF_PREPUB. 2017. 〈hal-01568243〉

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