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Seminars
2.30pm Wednesday 2 September 2009, Seminar room M345
School of Mathematical Sciences Colloquium
Discrete random matrices
Terry Tao (2009 Clay-Mahler lecturer and 2006 Fields medal winner)
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.
A full house was in attendance, augmented by numerous other universities connecting remotely via the Access Grid. We thank Terry for his excellent talk, and the sponsors AMSI, Clay Institute, and the Australian Mathematical Society. Professor Terry Tao is pictured with Head of School, Professor Kate Smith-Miles, and colloquium convenor, Dr. Ian Wanless, ringing the traditional bell to indicate the start of a colloquium.
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