Universality and fine zero spacing on general sets

By Vilmos Totik. 2009

103 citations recorded by the source corpus.

A recent approach of D. S. Lubinsky yields universality in random matrix theory and fine zero spacing of orthogonal polynomials under very mild hypothesis on the weight function, provided the support of the generating measure μ is [-1,1]. This paper provides a method with which analogous results can be proven on general compact subsets of R. Both universality and fine zero spacing involves the equilibrium measure of the support of μ. The method is based on taking polynomial inverse images, by which results can be transferred from [-1,1] to a system of intervals, and then to general sets.

Subfields: Applied Mathematics, Discrete Mathematics and Combinatorics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/a63d609df5dea6372b983e0237de82ce55be8df9

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In Applied Mathematics

In Discrete Mathematics and Combinatorics

In Statistics and Probability

Citations in the corpus

Christoffel Functions and Universality in the Bulk for Multivariate Orthogonal Polynomials (2013, background): “These arise in analysis of random matrices associated with unitary ensembles and, for compactly supported µ, may be reduced to the limit lim n→∞ Kn ( x + aµ ′(x) nω(x) , x + bµ ′(x) nω(x) ) Kn(x, x) = sinπ(a− b) π(a− b) , uniformly for a, b in compact subsets of the real line.”
Universality limits in the bulk for varying measures (2008, methodology): “It was subsequently extended to regular measures on arbitrary compact subsets of the real line using a host of other ideas by Barry Simon [47] and Vili Totik [ 53 ].”