2D random geometry from an i.i.d. field
Lingfu Zhang, Caltech
Abstract: On Z^2, assign an i.i.d. nonnegative random weight to each edge. The distance between two points is defined as the minimum total weight over all paths connecting them, which induces a random metric on Z^2. A central problem in this area is the Strong KPZ Universality Conjecture, which predicts that this random metric converges to a universal random directed metric on R^2. I will discuss recent developments that reveal rich and surprising geometric properties of such random metrics (on Z^2 or R^2). These 2D geometries are also closely connected to a broad class of probabilistic models, from random growth to interacting particles. I will explain how geometric viewpoints can provide new insights into resolving open problems in these related models. No prior knowledge in this topic is assumed.
Tea and refreshments available from 3:00-3:25 p.m. in the Assmus Conference Room (CU 212).
