# First-passage percolation with exponential times on a ladder - Mathematics > Probability

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Abstract: 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 timesare exponentially i.i.d. with mean 1. We find an appropriate Markov chain tocalculate an explicit expression for the time constant whose numerical value isapproximately 0.6827. This time constant is the long-term average inverse speedof the process. We also calculate the average residual time.

Author: ** Henrik Renlund**

Source: https://arxiv.org/