Decorrelation Estimates for the Eigenlevels of the Discrete Anderson Model in the Localized Regime

2010/04/30 by Frédéric Klopp
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Decorrelation #Dimension (graph theory) #Eigenvalues and eigenvectors #Independence (probability theory) #Mathematics #Physics #Pure mathematics #Quantum chaos and dynamical systems #Quantum mechanics #Spectral Theory in Mathematical Physics #Statistical physics #Statistics #Work (physics) #math-ph #math.MP

paper · pdf · doi:10.1007/s00220-011-1203-3

arxiv created 2010/09/05 · openalex publication_date 2011/02/11 · arxiv updated 2015/05/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

The purpose of the present work is to establish decorrelation estimates for the locally renormalized eigenvalues of the discrete Anderson model near two distinct energies inside the localization region. In dimension one, we prove these estimates at all energies. In higher dimensions, the energies are required to be sufficiently far apart from each other.

Citations

• Correlation Estimates in the Anderson Model
• Fine Structure of the Zeros of Orthogonal Polynomials, I. A Tale of Two Pictures
• Generalized Eigenvalue-Counting Estimates for the Anderson Model