Large deviations in first-passage percolation
type: Item
instance of: scholarly article
title: Large deviations in first-passage percolation
zbMATH Open document ID: 1038.60093
author: Yunshyong Chow
author: Y. Zhang
published in: The Annals of Applied Probability
publication date: 2004-03-30T00:00:00Z
review text: A specific probability space and measure are associated with nonnegative independent identically distributed random variables which are attached to normalized edges of a graph in (\(d>2\))-dimensional space. Each sample path between two vertices is an alternating sequence of vertices and edges with fixed end-points. Among various passage times, the face-face and point-point first-passage times are of major interest. The paper focuses on their limiting behaviour when the number of edges grows to infinity. Most limit behaviors in first passage percolation are obtained by using subadditive arguments which do not work in the limit. Technical Theorems 1-3 resolve this difficulty by employing the min-cut and max-flow theorems and setting up a multi-subadditive argument.
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 82B43
zbMATH DE Number: 2063753
zbMATH Keywords: first-passage percolation
zbMATH Keywords: large deviations
zbMATH Keywords: random variables on graphs
zbMATH Keywords: dynamics on graphs
reviewed by: Piotr Garbaczewski
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aoap/1069786513
OpenAlex ID: W1987057244
cites work: Probability
cites work: First-passage percolation, network flows and electrical resistances
cites work: Q5519643
cites work: Q3738376
cites work: First-passage percolation on the square lattice
cites work: Supercritical behaviors in first-passage percolation
DOI: 10.1214/AOAP/1069786513
description: scientific article; zbMATH DE number 2063753