Large N limit of fuzzy geometries coupled to fermions

TL;DR

This paper investigates the large N behavior of fermion-coupled fuzzy geometries modeled by multi-trace matrix ensembles, proving spectral density convergence and analyzing fermionic effects in spectral estimators.

Contribution

It introduces fermionic contributions into large N fuzzy geometry ensembles and proves spectral density convergence, advancing understanding of spectral properties in these models.

Findings

Spectral density converges in large N limit for these ensembles.

Fermionic effects are incorporated into spectral analysis.

Spectral estimators are studied for finite spectral triples.

Abstract

In this paper we present an analysis of the large N limit of a family of quartic Dirac ensembles based on (0, 1) fuzzy geometries that are coupled to fermions. These Dirac ensembles are examples of single-matrix, multi-trace matrix ensembles. Additionally, they serve as examples of integer-valued $\beta$-ensembles. Convergence of the spectral density in the large N limit for a large class of such matrix ensembles is proven, improving on existing results. The main results of this paper are the addition of the fermionic contribution in the matrix ensemble and the investigation of spectral estimators for finite dimensional spectral triples