Geodesics in first passage percolation

By Christopher E. Hoffman. 2005

101 citations recorded by the source corpus.

We consider a wide class of ergodic first passage percolation processes on I? and prove that there exist at least four one-sided geodesies 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 H?ggstr?m 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 geodesies and that coexistence is possible in a two-color Richardson's growth model.

Subfields: Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/61782427546068f54f6721baae684e4da31a5031

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In Mathematical Physics

In Statistics and Probability

Citations in the corpus

Stationary cocycles and Busemann functions for the corner growth model (2015, methodology): “Distinct from this line of work is Hoffman’s use of Busemann functions to study competition under more gener al weight distributions [31, 32].”
Quenched invariance principle for simple random walk on percolation clusters (2005, methodology): “⊓⊔ Interestingly, a variant of the above strategy for controlling the corrector in d = 2 has independently been developed by Chris Hoffman [25] to control the geodesics in the first-passage percolation onZ2.”
50 years of first passage percolation (2015, methodology): “These functions were first exploited in FPP in the important papers of Hoffman [101,102], and they allow one to obtain some information about geodesics without the unproven assumptions (for example, positive curvature of the limiting shape) of Newman.”