First passage percolation and escape strategies1. Issue 3 (23rd May 2014) - Andjel, Enrique D.
Abstract Consider first passage percolation on ℤd with passage times given by i.i.d. random variables with common distribution F. Let tπ(u, v) be the time from u to v for a path π and t(u, v) the minimal time among all paths from u to v. We ask whether or not there exist points x, y∈ℤd and a semi‐infinite path π=(y0=y, y1, …) such that tπ(y, yn+1)<t(x, yn) for all n. Necessary and sufficient conditions on F are given for this to occur. When the support of F is unbounded, we also obtain results on the number of edges with large passage time used by geodesics. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 414–423, 2015