Universality Limits, Orthogonal Polynomials and Weighted Polynomial Approximation

我们发展了一种新的方法来证明涉及正交多项式的普适性极限。例如，我们允许权重为正的A.E.全局性的，并且在给定点连续的。对于固定重量的普遍性来说，这已经足够了。我们打算探索这种方法对紧集和非紧集上的权重的限制，以及对不同权重的限制。这种类型的通用限制出现在随机矩阵的理论及其应用中，包括数学物理中的各种主题。重要的是，我们需要以前强有力的全球性假设，比如分析性。现在，只需要做出微弱的局部和全球假设。

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.