Asymptotic ergodicity of the eigenvalues of random operators in the localized phase
From the author's abstract: The author proves that, for a general class of random operators, the family of the unfolded eigenvalues in the localization region is asymptotically ergodic in the sense of \textit{N. Minami} [Special issue: Spectra of random operators and related topics. RIMS Kôkyûroku Bessatsu B27, 169 p. (2011; Zbl 1255.60004)]. Minami conjectured this to be the case for the discrete Anderson model in the localized regime. The author also provides a local analogue of this result. From the asymptotic ergodicity, one can recover the statistics of the level spacings as well as a number of other spectral statistics. The proof relies on the analysis developed by \textit{F. Germinet} and \textit{F. Klopp} [RIMS Kôkyûroku Bessatsu B27, 11--24 (2011; Zbl 1234.81075)].
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