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arXiv · 2109.12741

Spectral Statistics of Dirac Ensembles

Masoud Khalkhali·Nathan Pagliaroli
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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 non-Gaussian models this convolution property is also evident. In order to prove these results we show that a wide class of multi-trace multimatrix models have a genus expansion.

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Masoud Khalkhali, Nathan Pagliaroli. 2021-09-27. Spectral Statistics of Dirac Ensembles. https://doi.org/10.1063/5.0078267

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