The Mahler lectures are a biennial activity organised by the Australian Mathematical Society. In 2009 we have partnered with the Clay Mathematical Institute to combine the Mahler Lectures and the Clay Lectures into the 2009 Clay–Mahler Lecture Tour, with funding also from the Australian Mathematical Sciences Institute.

• 2nd September in Room 345, Building 28, Monash University and via the Access Grid, 2:30 pm
  specialist talk by Terence Tao (UCLA): Discrete Random Matrices

AGR Contact: Simon Clarke (simon.clarke@sci.monash.edu.au)
Other Clay–Mahler Access Grid events on the AMSI website

Abstract: Discrete Random Matrices

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 \pm1 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.