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The time constant and critical probabilities in percolation models

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	The time constant and critical probabilities in percolation models
2.	Creator	Author's name, affiliation, country	Leandro Pimentel; Ecole Polytechnique Federale de Lausanne
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Percolation; time constant; critical probabilities; Delaunay triangulations
3.	Subject	Subject classification	60K35;82D30
4.	Description	Abstract	We consider a first-passage percolation (FPP) model on a Delaunay triangulation $\mathcal{D}$ of the plane. In this model each edge $\mathbf{e}$ of $\mathcal{D}$ is independently equipped with a nonnegative random variable $\tau_\mathbf{e}$, with distribution function $\mathbb{F}$, which is interpreted as the time it takes to traverse the edge. Vahidi-Asl and Wierman \cite{VW90} have shown that, under a suitable moment condition on $\mathbb{F}$, the minimum time taken to reach a point $\mathbf{x}$ from the origin $\mathbf{0}$ is asymptotically $\mu(\mathbb{F})|\mathbf{x}|$, where $\mu(\mathbb{F})$ is a nonnegative finite constant. However the exact value of the time constant $\mu(\mathbb{F})$ still a fundamental problem in percolation theory. Here we prove that if $\mathbb{F}(0)<1-p_c^*$ then $\mu(\mathbb{F})>0$, where $p_c^*$ is a critical probability for bond percolation on the dual graph $\mathcal{D}^*$.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2006-08-07
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ecp.ejpecp.org/article/view/1210
10.	Identifier	Digital Object Identifier	10.1214/ECP.v11-1210
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 11
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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