Geodesics in First Passage Percolation

Details Geodesics in First Passage Percolation Geodesics in First Passage Percolation

2005-08-05

arxiv.org/abs/math/0508114v2

Mathematics

Probability

24 pages

Scientific paper

We consider a wide class of ergodic first passage percolation processes on Z^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 Haggstrom and Pemantle, Garet and Marchand, and Hoffman who proved that first passage percolation has at least two geodesics and that coexistence is possible in a two color Richardson's growth model.

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