A Central Limit Theorem for First Passage Percolation in the Slab

Abstract

We consider first-passage percolation on the edges of ${\mathbb{Z}}^2\times k,$ namely the slab of width $k$. Each edge is assigned independently a passage time of either 0 (with probability $1-p_c({\mathbb{S}}_k)$) or 1 ((with probability $p_c({\mathbb{S}}_k)$) where $p_c$ is the critical probability. We prove central limit theorems for point-to-point and point-to-line passage times. These generalize the results of [Kesten and Zhang] to non-planar graphs.

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