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

Eckhard Schlemm
2011 Journal of Applied Probability  
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
more » ... closely related Markov chain which can be used to explicitly calculate the asymptotic variance in the central limit theorem.
doi:10.1239/jap/1308662633 fatcat:vqjjtt4wprhoxm7ii5lx4ntj5a