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Infinite geodesics, competition interfaces and the second class particle in the scaling limit

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arxiv 2112.06849 v3 pith:4I5DVNJ4 submitted 2021-12-13 math.PR math-phmath.MP

classification math.PRmath-phmath.MP
keywords competitiongeodesicsinfiniteclassdirectedinterfaceinterfaceslandscape
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We establish fundamental properties of infinite geodesics and competition interfaces in the directed landscape. We construct infinite geodesics in the directed landscape, establish their uniqueness and coalescence, and define Busemann functions. We then define competition interfaces in the directed landscape. We prove the second class particle in tasep converges under KPZ scaling to a competition interface. Under suitable conditions, we show the competition interface has an asymptotic direction, analogous to the speed of a second class particle, and determine its law. Moreover, we prove the competition interface has an absolutely continuous law on compact sets with respect to infinite geodesics.

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  1. Quasi-geodesics in integrable and non-integrable exclusion processes

    math.PR 2024-12 conditional novelty 7.0 of 10

    For TASEP, the backward geodesic endpoint converges to the argmax of Airy_2 minus a parabola, and the same universal law is conjectured and numerically supported for ASEP and speed-changed ASEP.

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