FIRST PASSAGE PERCOLATION AND A MODEL FOR COMPETING SPATIAL GROWTH

An interacting particle system modelling competing growth on the Z(2) lattice is defined as follows. Each x is an element of Z(2) is in one of the states {0, 1,2}. 1's and 2's remain in their states for ever, w hile a 0 flips to a 1 (a 2) at a rate equal to the number of its neigh bours which are in state 1 (2). This is a generalization of the well-k nown Richardson model. 1's and 2's may be thought of as two types of i nfection, and 0's as uninfected sites. We prove that if we start with a single site in state 1 and a single site in state 2, then there is p ositive probability for the event that both types of infection reach i nfinitely many sites. This result implies that the spanning tree of ti me-minimizing paths from the origin in first passage percolation with exponential passage times has at: least two topological ends with posi tive probability.