The directed landscape

Duncan Dauvergne, Janosch Ortmann, Bálint Virág

Published 2018-12-02Version 1

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 the last passage geodesics converge to random functions with H\"older-$2/3^-$ continuous paths. This work completes the construction of the central object in the Kardar-Parisi-Zhang universality class, the directed landscape.