The directed landscape

Abstract

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.

78 pages, 6 figures

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Cited by in corpus (28)

• Exponents governing the rarity of disjoint polymers in Brownian last passage percolation
• Bulk properties of the Airy line ensemble
• Shift-invariance for vertex models and polymers
• Uniform convergence to the Airy line ensemble
• Three-halves variation of geodesics in the directed landscape
• Brownian absolute continuity of the KPZ fixed point with arbitrary initial condition
• The heat and the landscape I
• The stationary horizon and semi-infinite geodesics in the directed landscape
• Temporal Correlation in Last Passage Percolation with Flat Initial Condition via Brownian Comparison
• Global structure of semi-infinite geodesics and competition interfaces in Brownian last-passage percolation
• Convergence of the Environment Seen from Geodesics in Exponential Last-Passage Percolation
• Upper tail decay of KPZ models with Brownian initial conditions
• Airy process with wanderers, KPZ fluctuations, and a deformation of the Tracy--Widom GOE distribution
• Disjoint optimizers and the directed landscape
• Universality of deterministic KPZ
• Periodic TASEP with general initial conditions
• Edge Universality for Nonintersecting Brownian Bridges
• Brownian regularity for the KPZ line ensemble
• KPZ on torus: Gaussian fluctuations
• Tightness of Bernoulli Gibbsian line ensembles
• Fractal Geometry of the Valleys of the Parabolic Anderson Equation
• Mapping TASEP back in time
• Skew RSK dynamics: Greene invariants, affine crystals and applications to $q$-Whittaker polynomials
• Temporal increments of the KPZ equation with general initial data
• Coupling derivation of optimal-order central moment bounds in exponential last-passage percolation
• When the geodesic becomes rigid in the directed landscape
• Multi-point distribution of discrete time periodic TASEP
• Tightness of $(H,H^{RW})$-Gibbsian line ensembles