Alladi Ramakrishnan Hall

First-passage percolation, a model in the KPZ universality class

Arjun Krishnan

University of Rochester

First-passage percolation on Z^d was originally introduced to model the spread of fluid in a random porous medium. It a generalization of classical percolation theory, a model for geodesics of a random metric, and a member of the Kardar-Parisi-Zhang (KPZ) universality class for growth models. Other models in this universality class include random matrices, random tilings and asymptotic representation theory. The main object of study in first-passage percolation is the passage-time T(x), the (random) time it takes for a fluid particle that starts at the origin to reach x, a point on the lattice. We will talk about a variational formula for the limiting behavior of the passage-time and its connections to stochastic homogenization. We will also talk about the mysterious minimizers of the variational formula ---the so-called Busemann functions--- and their connection to the universal KPZ scaling behavior.