Electronic Communications in Probability

First-passage percolation on width-two stretches with exponential link weights

Eckhard Schlemm

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Abstract

We consider the first-passage percolation problem on effectively one-dimensional graphs with vertex set $\{1,\dots,n\}\times\{0,1\}$ and translation-invariant edge-structure. For three of six non-trivial cases we obtain exact expressions for the asymptotic percolation rate $\chi$ by solving certain recursive distributional equations and invoking results from ergodic theory to identify $\chi$ as the expected asymptotic one-step growth of the first-passage time from $(0, 0)$ to $(n, 0)$.

Article information

Source
Electron. Commun. Probab., Volume 14 (2009), paper no. 41, 424-434.

Dates
Accepted: 6 October 2009
First available in Project Euclid: 6 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465234750

Digital Object Identifier
doi:10.1214/ECP.v14-1493

Mathematical Reviews number (MathSciNet)
MR2551852

Zentralblatt MATH identifier
1189.60132

Subjects
Primary: 60J05: Discrete-time Markov processes on general state spaces
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Keywords
First-passage percolation percolation rate Markov chains ergodicity

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Schlemm, Eckhard. First-passage percolation on width-two stretches with exponential link weights. Electron. Commun. Probab. 14 (2009), paper no. 41, 424--434. doi:10.1214/ECP.v14-1493. https://projecteuclid.org/euclid.ecp/1465234750


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