Summary: The purpose of this paper is to describe the connection between asymptotic formulas for random matrices and Szegö limit theorems. The paper will illustrate how the distribution formula for a random variable can be described asymptotically by the classical Szegö theorems and then in turn how the ideas of random matrix theory allow one to find explicit expressions for Fredholm determinants. Szegö type limit theorems for smooth symbols are in this way equivalent to certain distributions being normal. We will also give an example of a distribution computed via more general limit theorems that is not normal.
For the entire collection see [Zbl 0922.00026].