The directed landscape

By Duncan Dauvergne, Janosch Ortmann, B'alint Vir'ag. Acta Mathematica, 2018

167 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/9cce3e739341793a2526e7fb761a547f4d630f2c