Invariant Ensembles and Orthogonal Polynomials I
Mathematical Physics Seminar
4th November 2022, 10:00 am – 11:00 am
Fry Building, 2.04
We explain how all statistics of eigenvalues of random Hermitian matrices taken from an ensemble whose law is invariant under unitary conjugations can be expressed in terms of orthogonal polynomials for general weight functions. Then we show how those polynomials are encoded in the solution of a certain Riemann-Hilbert problem of complex function theory. This leads to a method for approximating the polynomials and hence also the eigenvalue statistics in the limit that the matrix size is large.