3:00–4:20 pm Eckhart Hall, Room 202
Random Planar Geometry and the Directed Landscape
Consider the lattice Z^2, and assign length 1 or 2 to every edge by flipping a series of independent fair coins. This gives a random weighted graph, and looking at distances in this graph gives a random planar metric. This model, along with most natural models of random planar metrics and random interface growth (the so-called `KPZ universality class'), is expected to converge to a universal scaling limit: the directed landscape. The goal of this talk is to introduce this object, describe some of its properties, and describe at least one model where we can actually prove convergence.