PC Seminar: Surviving from the tip of a cone

Abstract: In two-type first passage percolation on the square lattice, two entities compete to capture the sites of the lattice. The entities spread between nearest neighbor sites at times specified by random passage times associated with the edges. We consider the case when both types have the same passage time distribution, with one type starting at the origin and the other from an infinite cone with tip at the origin. Can the type starting at the origin grow unboundedly? We give a partial answer to this question in terms of the slope of the cone.

This is a seminar in our seminar series on Probability and Combinatorics (PC).