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

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

2012-01-21

arxiv.org/abs/1201.4482v1

2009, Electron. Commun. Probab. 14, 424-434

Mathematics

Probability

10 pages, one table

Scientific paper

10.1214/ECP.v14-1493

We consider the first-passage percolation problem on effectively one-dimensional graphs with vertex set {1,...,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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