Error analysis of free probability approximations to the density of   states of disordered systems
  Theoretical studies of localization, anomalous diffusion and ergodicity breaking require solving the electronic structure of disordered systems. We use free probability to approximate the ensemble- averaged density of states without exact diagonalization. We present an error analysis that quantifies the accuracy using a generalized moment expansion, allowing us to distinguish between different approximations. We identify an approximation that is accurate to the eighth moment across all noise strengths, and contrast this with the perturbation theory and isotropic entanglement theory. 
Jiahao Chen (1), Eric Hontz (1), Jeremy Moix (1), Matthew Welborn (1),   Troy Van Voorhis (1), Alberto Su\'arez (2), Ramis M...
cond-mat.dis-nn math.ST physics.chem-ph quant-ph stat.TH