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June 2011 On the Markov transition kernels for first passage percolation on the ladder
Eckhard Schlemm
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J. Appl. Probab. 48(2): 366-388 (June 2011). DOI: 10.1239/jap/1308662633

Abstract

We consider the first passage percolation problem on the random graph with vertex set N x {0, 1}, edges joining vertices at a Euclidean distance equal to unity, and independent exponential edge weights. We provide a central limit theorem for the first passage times ln between the vertices (0, 0) and (n, 0), thus extending earlier results about the almost-sure convergence of ln / n as n → ∞. We use generating function techniques to compute the n-step transition kernels of a closely related Markov chain which can be used to explicitly calculate the asymptotic variance in the central limit theorem.

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Eckhard Schlemm. "On the Markov transition kernels for first passage percolation on the ladder." J. Appl. Probab. 48 (2) 366 - 388, June 2011. https://doi.org/10.1239/jap/1308662633

Information

Published: June 2011
First available in Project Euclid: 21 June 2011

zbMATH: 1223.60054
MathSciNet: MR2840305
Digital Object Identifier: 10.1239/jap/1308662633

Subjects:
Primary: 60J05, 60K35
Secondary: 33C90

Rights: Copyright © 2011 Applied Probability Trust

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Vol.48 • No. 2 • June 2011
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