Geodesics toward corners in first passage percolation

Abstract : For stationary first passage percolation in two dimensions, the existence and uniqueness of semi-infinite geodesics directed in particular directions or sectors has been considered by Damron and Hanson [4], Ahlberg and Hoffman [1], and others. However the main results do not cover geodesics in the direction of corners of the limit shape B, where two facets meet. We construct an example with the following properties: (i) the limiting shape is an octagon, (ii) semi-infinite geodesics exist only in the four axis directions, and (iii) in each axis direction there are multiple such geodesics. Consequently, the set of points of ∂B which are in the direction of some geodesic does not have all of B as its convex hull.
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Pré-publication, Document de travail
2017
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Contributeur : Quentin Berger <>
Soumis le : mercredi 27 septembre 2017 - 09:56:50
Dernière modification le : dimanche 17 décembre 2017 - 07:04:03

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  • HAL Id : hal-01595875, version 1

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Kenneth Alexander, Quentin Berger. Geodesics toward corners in first passage percolation. 2017. 〈hal-01595875〉

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