Multiple geodesics with the same direction

David Coupier (Laboratoire Paul Painlevé, UMR 8524, Université Lille 1)

Abstract


The directed last-passage percolation (LPP) model with independent exponential times is considered. We complete the study of asymptotic directions of infinite geodesics, started by Ferrari and Pimentel [5]. In particular, using a recent result of [3] and a local modification argument, we prove there is no (random) direction with more than two geodesics with probability 1.

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Pages: 517-527

Publication Date: September 26, 2011

DOI: 10.1214/ECP.v16-1656

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