Informal Friday Seminar: Feng -- Gaussian Random Matrices, Orthogonal Polynomials, and Skew-Orthogonal Polynomials

Title: Gaussian Random Matrices, Orthogonal Polynomials, and Skew-Orthogonal
Polynomials.  

Abstract: We will introduce the fundamental structures of Gaussian unitary ensemble
(GUE), Gaussian orthogonal ensemble (GOE) and Gaussian symplectic ensemble (GSE).  The
GUE exhibits a determinantal structure, which is closely related to the theory of
orthogonal polynomials, while the GOE and GSE have Pfaffian structures, connected to
skew-orthogonal polynomials.  We will also present some classical results such as Wigner
semicircle law, and the Tracy-Widom law regarding the largest eigenvalues.  

— Renjie Feng