First-passage percolation with exponential times on a ladder

Authors:
Henrik Renlund
Affiliations:
Mathematics department, uppsala university, po box 480, 751 06 uppsala, sweden (e-mail: renlund@math.uu.se)
Venue:
Combinatorics, Probability and Computing
Year:
2010

Citing 2
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Abstract

We consider first-passage percolation on a ladder, i.e., the graph ℕ × {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 ≈0.6827. This time constant is the long-term average inverse speed of the process. We also calculate the average residual time.