Multiple geodesics with the same direction

2011/04/07 by David Coupier, Coupier, David · 2 citations
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1104.1321

openalex publication_date 2011/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \citeFP. In particular, using a recent result of \citeCH2 and a local modification argument, we prove there is no (random) direction with more than two geodesics with probability 1.

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• Random Trees in Hyperbolic FPP
• Strong existence and uniqueness of the tilt-indexed Busemann process in the planar corner growth model

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