Year: 2025
Type: article
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, semi-infinite geodesics with intervals of asymptotic directions, 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 service stations at strictly positive speed.
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,990
Funders: National Science Foundation, Simons Foundation, Wisconsin Alumni Research Foundation, Carnegie Mellon University, Knut och Alice Wallenbergs Stiftelse, Université Paris Diderot, Fondation Sciences Mathématiques de Paris, Engineering and Physical Sciences Research Council, Division of Mathematical Sciences
Awards: G137891083, Growth and Motion in a Random Medium, Growth and Motion in a Random Medium, G4874825879, G5615800993, Random Walks in Random Potentials, Growth and Motion in a Random Medium, G6421992757, Particle systems, growth models and their probabilistic structures, G6864778645, G736543187, G759671407, G7947662707
OpenAlex ID: W4416420937