Decorrelation Estimates for Random Discrete Schrödinger Operators in Dimension One and Applications to Spectral Statistics

2014/09/30 by Christopher Shirley
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Combinatorics #Decorrelation #Dimension (graph theory) #Mathematical analysis #Mathematics #Numerical methods in inverse problems #Physics #Spectral Theory in Mathematical Physics #Statistical physics #Statistics #Stochastic process #math-ph #math.MP

paper · pdf · doi:10.1007/s10955-014-1168-7

arxiv created 2014/09/30 · openalex publication_date 2014/12/24 · arxiv updated 2015/06/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The purpose of the present work is to establish decorrelation estimates at distinct energies for some random Schrödinger operator in dimension one. In particular, we establish the result for some random operators on the continuum with alloy-type potential. These results are used to give a description of the spectral statistics.

Citations

• Bootstrap Multiscale Analysis and Localization¶in Random Media
• Generalized Eigenvalue-Counting Estimates for the Anderson Model
• Asymptotic ergodicity of the eigenvalues of random operators in the localized phase