First passage percolation and escape strategies |
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| Authors: | Enrique D Andjel Maria E Vares |
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| Institution: | 1. LATP URA 225/CNRS, Université d'Aix‐Marseille, 39, rue Joliot Curie, France;2. DME, Instituto de Matemática, Universidade Federal do Rio de Janeiro, Av. Athos da Silveira Ramos 149, Rio de Janeiro, RJ, Brasil |
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| Abstract: | Consider first passage percolation on  with passage times given by i.i.d. random variables with common distribution F. Let  be the time from u to v for a path π and  the minimal time among all paths from u to v. We ask whether or not there exist points  and a semi‐infinite path  such that  for all n. Necessary and sufficient conditions on F are given for this to occur. When the support of F is unbounded, we also obtain results on the number of edges with large passage time used by geodesics. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 414–423, 2015 |
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| Keywords: | first passage percolation escape strategy geodesic |
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