  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
