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2009 First-passage percolation on width-two stretches with exponential link weights
Eckhard Schlemm
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Electron. Commun. Probab. 14: 424-434 (2009). DOI: 10.1214/ECP.v14-1493


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 $(n, 0)$.


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Eckhard Schlemm. "First-passage percolation on width-two stretches with exponential link weights." Electron. Commun. Probab. 14 424 - 434, 2009.


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

zbMATH: 1189.60132
MathSciNet: MR2551852
Digital Object Identifier: 10.1214/ECP.v14-1493

Primary: 60J05
Secondary: 60K35

Keywords: ergodicity , First-passage percolation , Markov chains , percolation rate

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