Existence and continuity of the flow constant in first passage percolation
Existence and continuity of the flow constant in first passage percolation
复制标题
第一通道渗流中流量常数的存在性和连续性
DOI：
10.1214/18-ejp214
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Marie Th'eret
中科院分区：
文献类型：
--
作者：
Raphael Rossignol;Marie Th'eret
我们考虑Z^d上i.i.d的第一通道渗透模型，其中我们将在[0，+ $\infty$]（包括+ $\infty$）上具有共同分布G的i.i.d随机变量族与图的边缘相关联。时间常数与研究具有最小权重的一维路径（即测地线）有关，而流量常数与研究具有最小权重的（d—1）维曲面有关。在本文中，我们研究了流动常数在G({+$\infty$}) < p c (d)的唯一假设下的存在性（特别是在没有任何矩假设的情况下），一些自然最大流动对该常数的收敛性，以及该常数对分布G的连续性。
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.