Anomalous geodesics in the inhomogeneous corner growth model

2024/08/23 by Elnur Emrah, Emrah, Elnur, Christopher Janjigian +3 · 1 citation
Computer Science · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2408.13382

openalex publication_date 2024/08/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study Busemann functions, semi-infinite geodesics, and competition interfaces in the exactly solvable last-passage percolation with inhomogeneous exponential weights. New phenomena concerning geodesics arise due to inhomogeneity. These include novel Busemann functions associated with flat regions of the limit shape and thin rectangles, undirected semi-infinite geodesics, non-trivial axis-directed geodesics, intervals with no geodesic directions, and isolated geodesic directions. We further observe a new dichotomy for competition interfaces and second-class customers in a series of memoryless continuous-time queues with inhomogeneous service rates: a second class customer either becomes trapped or proceeds through the queue at strictly positive speed.

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