A Central Limit Theorem for First Passage Percolation in the Slab

Abstract

We consider first-passage percolation on the edges of Z 2 × {1, • • • , k}, namely the slab S k of width k. Each edge is assigned independently a passage time of either 0 (with probability pc(S k )) or 1 ( with probability 1 − pc(S k )) where pc is the critical probability for Bernouilli percolation. We prove central limit theorems for point-to-point and point-to-line passage times. These generalize the results of Kesten and Zhang [3] to non-planar graphs.