We have developed a new approach to proving universality limits involving orthogonal polynomials. We allow, for example, the weight to be positive a.e. globally, and continuous at a given point. That is enough for universality for a fixed weight. We intend to explore the limits of this method for weights on compact and non-compact sets, as well as for varying weights.
Universality limits of this type arise in the theory of random matrices and its applications, which include various topics in mathematical physics. The significance is that previously strong global hypotheses were required, such as analyticity. Now only weak local and global assumptions are required.
