Tomas Berggren: A Riemann-Hilbert Problem Approach to Mesoscopic Fluctuations for the CUE
Presentation of master's thesis in mathematics.
Time: Wed 2015-06-17 11.30 - 12.30
Location: Room 32, House 5, Kräftriket, Department of Mathematics, Stockholm University
Abstract:
In this thesis we will consider a particular probability measure, the Circular Unitary Ensemble, which is a famous model within Random Matrix theory.
We will give new proofs of two central limit theorem's associated to this measure. The proofs are based on the fact that the moment generating function of a linear statistic can be written as a Fredholm determinant of an integrable operator. With a Riemann-Hilbert problem approach, it is possible to evaluate the determinant asymptotically.