The Loop Equations of Random Matrices
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
Bagels, cookies, coffee and soda will be provided.
See you there!