| We consider first-passage percolation on the graph ℤ x {-hn,-hn+1,........hn}d-1 where each edge has an i.i.d. nonnegative weight. The passage time for a path is defined as the sum of weights of all the edges in that path and the first-passage time between two vertices is defined as the minimum passage time over all paths joining the two vertices. We will show that the first-passage time Tn between the origin and the vertex (n,0,......,0) satisfies a Gaussian CLT as long as hn = o(n) ∂ with <1/(d+1). The proof will be based on a decomposition of Tn as a sum of independent random variables and a renormalization type argument.
This is a joint work with Sourav Chatterjee. |