# Upper large deviations for the maximal flow through a domain of $olds{mathbb{R}^d}$ in first passage percolation - Mathematics > Probability

Upper large deviations for the maximal flow through a domain of $olds{mathbb{R}^d}$ in first passage percolation - Mathematics > Probability - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

Abstract: We consider the standard first passage percolation model in the rescaledgraph $\mathbb {Z}^d-n$ for $d\geq2$ and a domain $\Omega$ of boundary $\Gamma$in $\mathbb {R}^d$. Let $\Gamma ^1$ and $\Gamma ^2$ be two disjoint opensubsets of $\Gamma$ representing the parts of $\Gamma$ through which some watercan enter and escape from $\Omega$. We investigate the asymptotic behavior ofthe flow $\phi n$ through a discrete version $\Omega n$ of $\Omega$ between thecorresponding discrete sets $\Gamma ^1 n$ and $\Gamma ^2 n$. We prove thatunder some conditions on the regularity of the domain and on the law of thecapacity of the edges, the upper large deviations of $\phi n-n^{d-1}$ above acertain constant are of volume order, that is, decays exponentially fast with$n^d$. This article is part of a larger project in which the authors prove thatthis constant is the a.s. limit of $\phi n-n^{d-1}$.

Autor: Raphaël Cerf, Marie Théret

Fuente: https://arxiv.org/