Geodesics in two-dimensional first-passage percolation
type: Item
instance of: scholarly article
title: Geodesics in two-dimensional first-passage percolation
zbMATH Open document ID: 0863.60097
author: Cristina Licea
author: Charles M. Newman
published in: The Annals of Probability
publication date: 1997-06-15T00:00:00Z
review text: The paper concerns the standard first-passage percolation on \(\mathbb{Z}^2\). The passage time \(T(r)\) for a finite path \(r\) defines the random metric \(T(u,v)\) on sites \(u,v\in \mathbb{Z}^2\), which is the infimum of \(T(r)\) over all \(r\) between \(u\) and \(v\). A finite or infinite path \(r\) is called geodesic if each segment \(r(u',v')\) provides \(T(u',v')\). The problem of coalescence of semiinfinite geodesics is considered. A part of the important conjecture that doubly infinite geodesics do not exist is proved.
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 82B44
Mathematics Subject Classification ID: 60D05
zbMATH DE Number: 926218
zbMATH Keywords: disordered Ising model
zbMATH Keywords: random metric
zbMATH Keywords: first-passage percolation
zbMATH Keywords: passage time
zbMATH Keywords: geodesics
zbMATH Keywords: doubly infinite geodesics
reviewed by: A. Khorunzhy
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1042644722
OpenAlex ID: W2011137156
cites work: Density and uniqueness in percolation
cites work: Q5519643
cites work: Q3738376
cites work: Percolation theory and first-passage percolation
cites work: Q4866049
cites work: Infinite clusters in percolation models
DOI: 10.1214/AOP/1042644722
description: scientific article; zbMATH DE number 926218