Title: Asymptotic expansion in beta matrix models (joint with Analysis Seminar)
Speaker: Gaëtan Borot
Speaker Info: Max-Planck Institute for Mathematics, Bonn
I will describe general techniques to establish all-order asymptotic expansion in Coulomb gases with a large number N of particles, that typically arise when considering the eigenvalues of random matrices. In particular, when the particles (or the eigenvalues) accumulate on a single segment, there is an asymptotic expansion in 1/N, but if they accumulate on several disjoint segments, there is a oscillatory asymptotic expansion due to particle tunneling and expressed in terms of theta functions and their derivatives. As an application, we can derive all-order asymptotics for some solutions of Toda chain and (skew) orthogonal polynomials, that would be difficult to obtain by standard Riemann-Hilbert techniques.Date: Wednesday, September 24, 2014
This is based on joint works with Guionnet and Kozlowski.