Edge Universality of Beta Ensembles
Abstract
We prove the edge universality of the beta ensembles for any , provided that the limiting spectrum is supported on a single interval, and the external potential is and regular. We also prove that the edge universality holds for generalized Wigner matrices for all symmetry classes. Moreover, our results allow us to extend bulk universality for beta ensembles from analytic potentials to potentials in class.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 November 2014
 DOI:
 10.1007/s002200142120z
 arXiv:
 arXiv:1306.5728
 Bibcode:
 2014CMaPh.332..261B
 Keywords:

 Mathematics  Probability;
 Mathematical Physics;
 15B52;
 82B44
 EPrint:
 87 pages