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On the Markov Transition Kernels for First Passage Percolation on the Ladder

2011
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Journal of Applied Probability
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We consider the first passage percolation problem on the random graph with vertex set N x {0, 1}, edges joining vertices at a Euclidean distance equal to unity, and independent exponential edge weights. We provide a central limit theorem for the first passage times l n between the vertices (0, 0) and (n, 0), thus extending earlier results about the almost-sure convergence of l n / n as n → ∞. We use generating function techniques to compute the n-step transition kernels of a closely related

doi:10.1239/jap/1308662633
fatcat:vqjjtt4wprhoxm7ii5lx4ntj5a