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The Loop Equations of Random Matrices

Tova Brown

Abstract: The loop equations of random matrix theory have been used for quite some time to obtain explicit formulas for map enumeration generating functions. I want to use them to count certain families of graphs embedded on Riemann surfaces. But putting these loop equations on a rigorous mathematical foundation takes considerable work. Ercolani and McLaughlin did this in 2007. In this talk, I will be giving a broad overview of the steps in this derivation, as well as motivation for why we want to do it. Probability measures, random matrix theory, linear algebra, asymptotics, Riemann-Hilbert problems, contour integrations, and more will take their respective parts in this drama.

16 October, 2013, at 12:00
Math 402.