UREM-ULB :
Unité de Recherche sur l’Enseignement des Mathématiques

UNIVERSITE LIBRE DE BRUXELLES
DEPARTEMENT DE MATHEMATIQUE

VRIJE UNIVERSITEIT BRUSSEL
DEPARTEMENT WISKUNDE

MATHEMATICS COLLOQUIUM

Holger DETTE Ruhr-Universitaet Bochum, Germany OPTIMAL DESIGNS, ORTHOGONAL POLYNOMIALS AND RANDOM MATRICES

The talk explains several relations between different areas of mathematics : mathematical statistics, random matrices and special functions. We give an introduction in the theory of optimal designs, which are used to improve the accuracy of statistical inference without performing additional experiments. It is demonstrated that for certain regression models orthogonal polynomials play an important role in the construction of optimal designs. In the next step these results are connected with some classical facts from random matrix theory. In the third part of this talk we discusss some new results on special functions and random matrices. In particular we analyse random band matrices, which generalize the classical Gaußschen ensemble. We show that the random eigenvalues of such matrices behave similarly as the deterministic roots of matrix orthogonal polynomials with varying recurrence coefficients. We study the asymptotic zero distribution of such polynomials and demonstrate that these results can be used to find the asymptotic properties of the spectrum of random band matrices.

Friday 1 March 2013 at 16:15

 ULB Campus Plaine – Building NO – 9th Floor
 Salle des Professeurs (2NO 906)
 Everybody is cordially welcome

Christine De Mol and Philippe Cara