Arno Kuijlaars: Products of random matrices

Abstract:

Eigenvalues and singular values of a  number of important random matrix models 
have a determinantal structure that reflects the built-in repulsion
between neighoring values. Because of the determinantal structure, 
many tools from linear algebra
and combinatorics become available to find explicit formulas, which 
can then be used to establish limiting result as the size of the matrices
tends to infinity.

It is a fairly recent discovery that the determinantal structure can
be preserved when taking products of random matrices. I will present 
this for the case of singular values. The resulting exact formulas
lead to a new class of scaling limits with Meijer G-functions.

The talk is based on joint works with Lun Zhang (Fudan), Mario Kieburg (Bielefeld)
and Dries Stivigny (Leuven).