Geodesics in first passage percolation

We consider a wide class of ergodic first passage percolation processes on .2 and prove that there exist at least four one-sided geodesics a.s. We also show that coexistence is possible with positive probability in a four-color Richardson.s growth model. This improves earlier results of Häggström and Pemantle [J. Appl. Probab. 35 (1995) 683.692], Garet and Marchand [Ann. Appl. Probab. 15 (2005) 298.330] and Hoffman [Ann. Appl. Probab. 15 (2005) 739.747] who proved that first passage percolation has at least two geodesics and that coexistence is possible in a two-color Richardson.s growth model.