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The directed landscape

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arxiv 1812.00309 v7 pith:3NKKFKXA submitted 2018-12-02 math.PR math-phmath.MP

Duncan Dauvergne , Janosch Ortmann , Balint Virag This is my paper · ORCID
classification math.PRmath-phmath.MP
keywords lastpassageairydirectedlandscapepercolationbrowniancentral
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The conjectured limit of last passage percolation is a scale-invariant, independent, stationary increment process with respect to metric composition. We prove this for Brownian last passage percolation. We construct the Airy sheet and characterize it in terms of the Airy line ensemble. We also show that last passage geodesics converge to random functions with Holder-2/3- continuous paths. This work completes the construction of the central object in the Kardar-Parisi-Zhang universality class, the directed landscape.

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