  We study discrete spectral quantities associated to Schr\"odinger operators
of the form $-\Delta_{\mathbb{R}^d}+V_N$, $d$ odd. The potential $V_N$ models a
highly disordered crystal; it varies randomly at scale $N^{-1} \ll 1$. We use
perturbation analysis to obtain almost sure convergence of the eigenvalues and
scattering resonances of $-\Delta_{\mathbb{R}^d}+V_N$ as $N \rightarrow
\infty$. We identify a stochastic and a deterministic regime for the speed of
convergence. The type of regime depends whether the low frequencies effects due
to large deviations overcome the (deterministic) constructive interference
between highly oscillatory terms.
