Dr Jon Warren (University of Warwick)

Random matrices, Stochastic Growth models and the KPZ equation.

I will base this talk on two pieces of joint work. One with Peter Windridge, the other with Neil O'Connell. Firstly I will show you how the distribution of a largest eigenvalue of certain random matrix ( in fact having a Wishart distribution) arises also in a simple stochastic growth model. In fact this growth model belongs to a large universality class, which includes mathematical models for interfaces as diverse as the edge of a burning piece of paper, or a colony of bacteria on a petri dish. The KPZ equation is a stochastic partial differential equation that also belongs to this universality class, and in the work with Neil we set out to construct an analogue, for the KPZ equation, for the second, third and so on largest eigenvalues of the random matrix.