Speaker
Description
Our main attention will be devoted to the normal matrices ensembles, which have many interesting applications (Laplacian growth, Diffusion limited aggregation). An important feature of the orthogonal polynomials ensembles of random matrices is that the joint probability density of their eigenvalues is represented by means of the determinants composed by Christoffel--Darboux (CD) kernels of orthogonal polynomials or their generalizations. For the normal matrices ensembles the corresponded CD kernel is taken for polynomials orthogonal with respect to an area measure. We show that for some special cases of the normal random matrices (related with discrete Painlevé equation) these polynomials are the multiple orthogonal polynomials. This fact makes their asymptotical analysis much easier.
