First-passage percolation with exponential times on a ladder

Details First-passage percolation with exponential times on a ladder First-passage percolation with exponential times on a ladder

2010-02-19

arxiv.org/abs/1002.3709v1

Combin. Probab. Comput., vol. 19, issue 4 (2010), 593-601

Mathematics

Probability

2 figures

Scientific paper

We consider first-passage percolation on a ladder, i.e. the graph {0,1,...}*{0,1} where nodes at distance 1 are joined by an edge, and the times are exponentially i.i.d. with mean 1. We find an appropriate Markov chain to calculate an explicit expression for the time constant whose numerical value is approximately 0.6827. This time constant is the long-term average inverse speed of the process. We also calculate the average residual time.

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