The directed landscape
Duncan Dauvergne, Janosch Ortmann, Bálint Virág
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.
Topics & Concepts
GeodesicMathematicsBrownian motionUniversality (dynamical systems)Statistical physicsMathematical analysisPure mathematicsMathematical physicsPhysicsStatisticsQuantum mechanicsRandom Matrices and ApplicationsStochastic processes and statistical mechanicsBayesian Methods and Mixture Models