Inverse tunneling estimates and applications to the study of spectral statistics of random operators on the real line
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Frédéric Klopp
Abstract.
We present a proof of a Minami type estimate for one-dimensional random Schrödinger operators valid at all energies in the localization regime provided a Wegner estimate is known to hold. The Minami type estimate is then applied to two models to obtain results on their spectral statistics. The heuristics underlying our proof of Minami type estimates is that close-by eigenvalues of a one-dimensional Schrödinger operator correspond either to eigenfunctions that live far away from each other in space or they come from some tunneling phenomena. In the second case, one can undo the tunneling and thus construct quasi-modes that live far away from each other in space.
Funding source: ANR
Award Identifier / Grant number: ANR-08-BLAN-0261-01
© 2014 by Walter de Gruyter Berlin/Boston
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Articles in the same Issue
- Frontmatter
- UC hierarchy and monodromy preserving deformation
- Vector-valued p-adic Siegel modular forms
- K-theoretic Schubert calculus for OG(n,2n+1) and jeu de taquin for shifted increasing tableaux
-
Strichartz estimates for partially periodic solutions to Schrödinger equations in
- Inverse tunneling estimates and applications to the study of spectral statistics of random operators on the real line
- Mean curvature flow of entire graphs in a half-space with a free boundary
- Ricci flow and the holonomy group
- Uniqueness of compact tangent flows in Mean Curvature Flow
- Even unimodular Lorentzian lattices and hyperbolic volume
- Algebraic points on Shimura curves of Γ0(p)-type
- Errata to Algebraic points on Shimura curves of Γ0(p)-type (J. reine angew. Math., DOI 10.1515/crelle-2012-0068)
- Property A and the operator norm localization property for discrete metric spaces
- Stable manifolds for holomorphic automorphisms
