Boris Khoruzhenko: Moments of random determinants: an exercise in Schur function expansion
Abstract:
We obtain the integer moments of the spectral determinant $|\det(zI-W)|^2$ of complex random matrices $W$ in terms of the characteristic polynomial of the Hermitian matrix $WW^*$ for the class of matrices $W=AU$ where $A$ is a given matrix and $U$ is random unitary. I will explain the motivation for this work (distribution of eigenvalues in the complex plane) and the technique used for evaluating the group integral (Schur function expansions).