Discrete Random Matrices -- 2009 Moursund Lectures, Day 3

Terence Tao, 2006 Fields Medal Recipient
University of California, Los Angeles
Lecture three of a three part series


Abstract: The spectral theory of continuous random matrix models (e.g. real or complex gaussian random matrices) has been well studied, and very
precise information on the distribution of eigenvalues and singular values is now known. But many of the results rely quite heavily on the special algebraic
properties of the matrix ensemble (e.g. the invariance properties with respect to the orthogonal or unitary group). As such, the results do not easily extend
to discrete random matrix models, such as the Bernoulli model of matrices with random ±1 signs as entries. Recently, however, tools from additive
combinatorics and elementary linear algebra have been applied to establish several results for such discrete ensembles, such as the circular law for the
distribution of eigenvalues, and also explicit asymptotic distributions for the least singular values of such matrices. We survey some of these developments
in this talk.


The Moursund lecures are an annual lecture series in which the University of Oregon brings a distinguished mathematician to campus. The lecture series is named after Andrew Moursund, who was the Math department's head from 1939 to 1970, and are partly paid for by an endowment formed by Moursund's widow (Lulu Moursund) and son (David Moursund).