### Résumé de communication

Résumé 292 :

**Optimal designs, orthogonal polynomials and random matrices**

__Dette, Holger__

*Ruhr-Universitaet Bochum*

The talk explains several relations between different areas of mathematics: Mathematical statistics, random matrices and special functions. We give a careful 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 discuss 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 proporties of the spectrum of random band matrices.