The directed landscape

Understand

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.