Spectral Statistics of Dirac Ensembles
Abstract
In this paper we find spectral properties in the large $N$ limit of Dirac operators that come from random finite noncommutative geometries. In particular for a Gaussian potential the limiting eigenvalue spectrum is shown to be universal regardless of the geometry and is given by the convolution of the semicircle law with itself. For simple nonGaussian models this convolution property is also evident. In order to prove these results we show that a wide class of multitrace multimatrix models have a genus expansion.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.12741
 Bibcode:
 2021arXiv210912741K
 Keywords:

 High Energy Physics  Theory;
 Mathematical Physics;
 Mathematics  Operator Algebras;
 Mathematics  Quantum Algebra;
 58B34;
 81Sxx;
 05Axx
 EPrint:
 5 figures, 24 pages