Title: Self-similarity in the eigenvalues of random unitary matrices
Speaker: Mark Meckes (Associate Professor, MAMS Department, Case Western Reserve University)
Abstract: In a statistical study of the observed relationship between eigenvalues of large random unitary matrices and zeros of the Riemann zeta function, Coram and Diaconis proposed a “self-similarity” phenomenon for random unitary eigenvalues. Roughly, they suggested that the eigenvalues of an n x n random matrix should be statistically indistinguishable from half the eigenvalues of a 2n x 2n random matrix, with suitable rescaling. I will present a rigorous result along these lines, joint with Elizabeth Meckes, and build up some of the general machinery needed for the proof.