Upper and lower bounds for the route length of first-passage percolation in Voronoi tessellations
type: Item
instance of: scholarly article
title: Upper and lower bounds for the route length of first-passage percolation in Voronoi tessellations
zbMATH Open document ID: 0802.60096
author: John C. Wierman
author: Mohammad Q. Vahidi-Asl
published in: Bulletin of the Iranian Mathematical Society
publication date: 1994-12-12T00:00:00Z
review text: The first passage percolation defined on a graph obtained from Voronoi tessellation of the plane, generated by a homogeneous Poisson process, is considered. The almost sure existence of the optimal path between arbitrary pair of vertices on the graph (the route for the first-passge time) is proved. This path realizes the infimum of the travel times between vertices. The upper and lower bounds for the route length divided by geometrical distance are proved as well.
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 82B43
zbMATH DE Number: 579698
zbMATH Keywords: first passage percolation
zbMATH Keywords: Voronoi tessellation
zbMATH Keywords: homogeneous Poisson process
zbMATH Keywords: almost sure existence
zbMATH Keywords: optimal path
zbMATH Keywords: travel times
zbMATH Keywords: upper and lower bounds for the route length
reviewed by: Yu. P. Virchenko
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 579698