Corpus ID: 237940136

Spectral Statistics of Dirac Ensembles

@inproceedings{Khalkhali2021SpectralSO,
  title={Spectral Statistics of Dirac Ensembles},
  author={Masoud Khalkhali and Nathan Pagliaroli},
  year={2021}
}
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… Expand
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References

SHOWING 1-10 OF 24 REFERENCES
Monte Carlo simulations of random non-commutative geometries
Random non-commutative geometries are introduced by integrating over the space of Dirac operators that form a spectral triple with a fixed algebra and Hilbert space. The cases with the simplest typesExpand
Matrix geometries and fuzzy spaces as finite spectral triples
A class of real spectral triples that are similar in structure to a Riemannian manifold but have a finite-dimensional Hilbert space is defined and investigated, determining a general form for theExpand
Topological Recursion and Random Finite Noncommutative Geometries
In this thesis, we investigate a model for quantum gravity on finite noncommutative spaces using the topological recursion method originated from random matrix theory. More precisely, we consider aExpand
On the spectral characterization of manifolds
We show that the first five of the axioms we had formulated on spectral triples suffice (in a slightly stronger form) to characterize the spectral triples associated to smooth compact manifolds. TheExpand
The Spectral Action Principle
Abstract:We propose a new action principle to be associated with a noncommutative space . The universal formula for the spectral action is where is a spinor on the Hilbert space, is a scale and aExpand
Scaling behaviour in random non-commutative geometries
Random non-commutative geometries are a novel approach to taking a non-perturbative path integral over geometries. They were introduced in arxiv.org/abs/1510.01377, where a first examination wasExpand
Formal multidimensional integrals, stuffed maps, and topological recursion
We show that the large N expansion in the multi-trace 1 formal hermitian matrix model is governed by the topological recursion of [Eynard and Orantin, 2007] with initial conditions. In terms of a 1dExpand
Noncommutative geometry and reality
We introduce the notion of real structure in our spectral geometry. This notion is motivated by Atiyah’s KR‐theory and by Tomita’s involution J. It allows us to remove two unpleasant features of theExpand
Noncommutative Geometry
Noncommutative Spaces It was noticed a long time ago that various properties of sets of points can be restated in terms of properties of certain commutative rings of functions over those sets. InExpand
Blobbed topological recursion
We describe the formalism and the properties of the blobbed topological recursion, which provides the general solution of a set of abstract loop equations. This procedure extends the topologicalExpand
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