School of Mathematical Sciences
Monday, June 8, 2015
Schreiber 006, 12:15
Random matrices: Gaps between eigenvalues
Gaps (or spacings) between consecutive eigenvalues of a random
hermitian matrix plays a central role in random matrix theory. When
Wigner used random matrix as a model in physics, it was the behavior of
the gaps that captured his attention. Another famous example is the
Dyson-Montgomery discussion connecting these gaps with gaps between
zeroes of the zeta function.
On the other hand, we still do not understand these gaps very
well at the microscopic level. For instance, it has only been
proved very recently by Tao and the speaker that for a random +-1
matrix, with high probability all gaps are positive.
this talk, we will discuss some recent progress in bounding these gaps,
based on purely combinatorial techniques, for very general classes of
random matrices. We will also present applications in both computer
science and numerical analysis (among others, solutions to questions by
Babai, and by Deker-Lee-Linial).
Joint work with H. Nguyen (OSU) and T. Tao (UCLA).
Coffee will be served at 12:00 before the lecture
at Schreiber building 006