Universality Limits for Random Matrices and de Branges Spaces of Entire Functions ✩

@inproceedings{Lubinsky2009UniversalityLF,
  title={Universality Limits for Random Matrices and de Branges Spaces of Entire Functions ✩},
  author={Doron S. Lubinsky},
  year={2009}
}
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 reproducing kernel, suitably dilated, may arise as a universality limit for sequences of measures on [−1, 1… CONTINUE READING