Philippe Moreillon: Disk counting statistics of the eigenvalues of truncated unitary matrices

Speaker
Philippe Moreillon, University of Geneva

Abstract
In this talk, I will present new results on the disk counting statistics of the eigenvalues of truncated unitary matrices. More specifically, if T is the upper-left submatrix of a Haar distributed unitary matrix of size (n+k) x (n+k), we prove that as n tends to infinity with k fixed, the associated moment generating function verifies asymptotics of the form exp(C_1 n + C_2 + o(1)), where the constants C_1 and C_2 are given in terms of the incomplete Gamma function. As we will see, our proof relies on the uniform asymptotics of the incomplete Beta function. This talk is based on a joint work with Christophe Charlier and Yacin Ameur.