Universality limits for random matrices and de Branges spaces of entire functions

作者：Lubinsky D S^*

来源：Journal of Functional Analysis, 2009, 256(11): 3688-3729.

DOI：10.1016/j.jfa.2009.02.021

• Random matrices
• Universality limits
• de Branges spaces
• Orthogonal polynomials

We prove that de Branges spaces of entire functions describe universality limits in the bulk for random matrices, in the unitary case. In particular, under mild conditions on a measure with compact support, We show that each possible universality limit is the reproducing kernel of a de Branges space of entire functions that equals a classical Paley-Wiener space. We also show that any such producing kernel, suitably dilated. may arise as a universality limit for sequences of measures on [-1 ,1].

• 出版日期2009-6-1