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November 2003 Large deviations in first-passage percolation
Yunshyong Chow, Yu Zhang
Ann. Appl. Probab. 13(4): 1601-1614 (November 2003). DOI: 10.1214/aoap/1069786513

Abstract

Consider the standard first-passage percolation on \Zd, d2. Denote by ϕ0,n the face--face first-passage time in [0,n]d. It is well known that limnϕ0,nn=μ(F)a.s. and in L1, where F is the common distribution on each edge. In this paper we show that the upper and lower tails of ϕ0,n are quite different when μ(F)>0. More precisely, we can show that for small ε>0, there exist constants α(ε,F) and β(ε,F) such that limn1nlogP(ϕ0,nn(με))=α(ε,F) and limn1ndlogP(ϕ0,nn(μ+ε))=β(ε,F).

Citation

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Yunshyong Chow. Yu Zhang. "Large deviations in first-passage percolation." Ann. Appl. Probab. 13 (4) 1601 - 1614, November 2003. https://doi.org/10.1214/aoap/1069786513

Information

Published: November 2003
First available in Project Euclid: 25 November 2003

zbMATH: 1038.60093
MathSciNet: MR2023891
Digital Object Identifier: 10.1214/aoap/1069786513

Subjects:
Primary: 60K35

Keywords: First-passage percolation , large deviations

Rights: Copyright © 2003 Institute of Mathematical Statistics

Vol.13 • No. 4 • November 2003
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