Recent progress on products of random matrices
Bielefeld University and LPTMS Orsay
Lundi 04/05/2015, 11h00
Salle Claude Itzykson, Bât. 774, Orme des Merisiers
In this talk I will report on recent progress regarding the singular value distribution for products of independent Gaussian random matrices. They are given by a determinantal point processes involving special functions, the so-called MeijerG-function. Despite this fact the corresponding kernel, in terms of which all correlation functions of singular values can be expressed, shares some nice features with the kernel of orthogonal Laguerre polynomials for a single random matrix. For M products of random matrices in the limit of large matrix size a new class of M limiting kernels is found that is universal. It generalises the kernel of Borodin in bi-orthogonal ensembles. Moreover, the exact solution of this random matrix ensemble allows us to derive the normal distribution of all Lyapunov exponents including corrections.