The directed landscape

VIENNA PROBABILITY SEMINAR

The directed landscape is a random directed metric' on the spacetime plane that arises as the scaling limit of integrable models of last passage percolation. It is expected to be the universal scaling limit for all models in the KPZ universality class for random growth. In this talk, I will describe its construction in terms of the Airy line ensemble via an isometric property of the Robinson-Schensted-Knuth correspondence, and discuss some surprising Brownian structures that arise from this construction. Based on joint work with M. Nica, J. Ortmann, B. Virag, and L. Zhang.