Session B5 - Random Matrices
July 14, 15:00 ~ 15:25
Self-similarity in the spectra of random unitary matrices
Case Western Reserve University, USA - firstname.lastname@example.org
I will present a rigorous result roughly stating that, for a range of mesoscopic scales, the eigenvalues of an $n \times n$ random unitary matrix are statistically indistinguishable from those of a $2n \times 2n$ matrix, suitably rescaled. This result is inspired by a conjecture made by Coram and Diaconis in a statistical study of the relationship between eigenvalues of large random unitary matrices and zeroes of the Riemann zeta function.
Joint work with Elizabeth Meckes (Case Western Reserve University).