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Theoretical studies of localization, anomalous diffusion and ergodicitybreaking require solving the electronic structure of disordered systems. We usefree probability to approximate the ensemble- averaged density of stateswithout exact diagonalization. We present an error analysis that quantifies theaccuracy using a generalized moment expansion, allowing us to distinguishbetween different approximations. We identify an approximation that is accurateto the eighth moment across all noise strengths, and contrast this with theperturbation theory and isotropic entanglement theory.

Error analysis of free probability approximations to the density of states of disordered systems