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 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.

arXiv comment5 figures, 24 pages, very minor changes

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Cited by in corpus (7)

• Bootstrapping Dirac Ensembles
• From Noncommutative Geometry to Random Matrix Theory
• Double scaling limits of Dirac ensembles and Liouville quantum gravity
• BV quantization of dynamical fuzzy spectral triples
• No-resonance conditions, random matrices, and quantum chaotic models
• Computational explorations of a deformed fuzzy sphere
• A ribbon graph derivation of the algebra of functional renormalization for random multi-matrices with multi-trace interactions