Existence and continuity of the flow constant in first passage percolation

Raphaël Rossignol; Marie Théret

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arXiv · 1707.08766

Existence and continuity of the flow constant in first passage percolation

Raphaël Rossignol·Marie Théret

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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, +$\infty$] (including +$\infty$). 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({+$\infty$}) < 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.

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Raphaël Rossignol, Marie Théret. 2017-07-27. Existence and continuity of the flow constant in first passage percolation. https://arxiv.org/abs/1707.08766

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