# Matrix theory

Monday, June 25, 2012 - 2:00pm - 3:15pm

Jonathan Novak (Massachusetts Institute of Technology)

The Harish-Chandra-Itzykson-Zuber integral is a remarkable special function which plays a key role in random matrix theory, where it enters into the description of the spectra of coupled random matrices, Hermitian Wigner matrices, and complex sample covariance matrices. As shown by Guionnet and Zeitouni, the leading asymptotics of the HCIZ integral can be characterized as the solution to a certain variational problem. I will present joint work with I. Goulden and M.

Wednesday, April 29, 2015 - 11:30am - 12:20pm

Paul Bourgade (Courant Institute of Mathematical Sciences)

Eugene Wigner has envisioned that the distributions of the eigenvalues of large Gaussian random matrices are new paradigms for universal statistics of large correlated quantum systems. These random matrix eigenvalues statistics supposedly occur together with delocalized eigenstates. In this lecture, I will explain recent developments proving this paradigm, for both eigenvalues and eigenvectors of random matrices.

Wednesday, April 29, 2015 - 10:20am - 11:10am

Jun Yin (University of Wisconsin, Madison)

Comparison method has been used in the proofs of many theorems in random matrix theory, e.g., bulk universality, edge universality of Wigner matrix, local circular law. In previous work, most comparison work is based on Lindeberg strategy. In this talk, we will introduce a new comparison method: continuous self consistent comparison method, and discuss its applications on random matrix theory.