  In condensed-matter, level statistics has long been used to characterize the
phases of a disordered system. We provide evidence within the context of a
simple model that in a disordered large-N gauge theory with a gravity dual,
there exist phases where the nearest neighbor spacing distribution of the
unfolded pole spectra of generic two-point correlators is Poisson. This closely
resembles the localized phase of the Anderson Hamiltonian. We perform two tests
on our statistical hypothesis. One is based on a statistic defined in the
context of Random Matrix Theory, the so-called $\bar{\Delta_3}$, or spectral
rigidity, proposed by Dyson and Mehta. The second is a $\chi$-squared test. In
our model, the results of both tests are consistent with the hypothesis that
the pole spectra of two-point functions can be at least in two distinct phases;
first a regular sequence and second a completely uncorrelated sequence with a
Poisson nearest neighbor spacing distribution.
