MathMeetings.net

Understanding the large dimension asymptotics of random matrices or related models such as random tilings has been a hot topic for the last twenty years within probability, mathematical physics, and statistical mechanics. Because such models are highly correlated, classical methods based on independent variables fail. Special cases have been studied in detail thanks to specific forms of the laws, such as determinantal laws. These lectures will investigate a general class of models using the so called Dyson-Schwinger equations or generalizations such as Nekrasov's equations. The idea is similar to Stein's method in that the observables are approximate solutions of equations that can be solved asymptotically.

Alice Guionnet (Lyon) will give ten main lectures, divided into two per day. Besides these lectures there will be supplementary lectures by other senior researchers attending the school, including:

Charles Bordenave (Toulouse)

Gaetan Borot (Bonn)

Paul Bourgade (NYU)

Vadim Gorin (MIT)

Sylvia Serfaty (NYU)

This school is intended for graduate students and postdocs who are starting to learn random matrix theory and have some background in probability. Lecture notes will be distributed in advance for preparation and tutorials and problem sessions will be run throughout the school.