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October 2008 Geodesics in first passage percolation
Christopher Hoffman
Ann. Appl. Probab. 18(5): 1944-1969 (October 2008). DOI: 10.1214/07-AAP510

Abstract

We consider a wide class of ergodic first passage percolation processes on ℤ2 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.

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Christopher Hoffman. "Geodesics in first passage percolation." Ann. Appl. Probab. 18 (5) 1944 - 1969, October 2008. https://doi.org/10.1214/07-AAP510

Information

Published: October 2008
First available in Project Euclid: 30 October 2008

zbMATH: 1153.60055
MathSciNet: MR2462555
Digital Object Identifier: 10.1214/07-AAP510

Subjects:
Primary: 60K35, 82B43

Rights: Copyright © 2008 Institute of Mathematical Statistics

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Vol.18 • No. 5 • October 2008
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