Asymptotic ergodicity of the eigenvalues of random operators in the localized phase

• 成果类型: Article
• 署名作者: Klopp, Frederic
• 署名单位: Universite Paris 13
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-012-0415-6
• 发表日期: 2013
• 页码: 867-909
• 关键词: density-of-states; SCHRODINGER-OPERATORS

摘要

We prove 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 Minami (Spectra of random operators and related topics, 2011). Minami conjectured this to be the case for discrete Anderson model in the localized regime. We also provide a local analogue of this result. From the asymptotics ergodicity, one can recover the statistics of the level spacings as well as a number of other spectral statistics. Our proofs rely on the analysis developed in Germinet and Klopp (Spectral statistics for random Schrodinger operators in the localized regime, 2010).