The directed landscape from Brownian motion

ESB 4127

The KPZ (Kardar-Parisi-Zhang) universality class is a loose term for a collection of random interface growth models and random planar metrics that exhibit the same behaviour under rescaling. Examples of models in this class include TASEP, last passage percolation, and the KPZ equation. The richest scaling limit of these models is the directed landscape, a random directed metric on the plane. In this talk, I will describe a new construction of the directed landscape from an infinite collection of Brownian motions and a version of the Robinson-Schensted-Knuth correspondence. Based on joint work with Balint Virag.