A Central Limit Theorem for First Passage Percolation in the Slab

We consider first-passage percolation on the edges of $$\mathbb{Z}$^2 \times k,$namelytheslabofwidth$k$. 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.