Smoothness of the density of states in the Anderson model at high disorder

DOI10.1007/BF01242138zbMath0644.60057MaRDI QIDQ1102627

Anton Bovier, Abel Klein, J. Fernando Perez, Massimo Campanino

Publication date: 1988

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

Anderson modelcharacteristic functionsupersymmetric replica trickconvergent cluster expansions

Mathematics Subject Classification ID

Random operators and equations (aspects of stochastic analysis) (60H25) Stochastic mechanics (including stochastic electrodynamics) (81P20)

Related Items

Supersymmetric measures and maximum principles in the complex domain. Exponential decay of green's functions ⋮ Supersymmetric cluster expansions and applications to random Schrödinger operators ⋮ The density of states in the Anderson model at weak disorder: A renormalization group analysis of the hierarchical model ⋮ Universal regularity of higher-dimensional disorder and density of states under non-local interactions. I: Infinite smoothness and localization ⋮ Smoothness of integrated density of states of the Anderson model on Bethe lattice in high disorder ⋮ Wegner-type bounds for a two-particle lattice model with a generic ``rough quasi-periodic potential ⋮ Smoothness of the integrated density of states on strips ⋮ Spectral statistics for random Schrödinger operators in the localized regime ⋮ A note on the analyticity of density of states ⋮ Supersymmetry and density of states of the magnetic schrödinger operator with a random potential revisited ⋮ Regularity of the density of states in the Anderson model on a strip for potentials with singular continuous distributions ⋮ Singularity of the density of states for one-dimensional chains with random couplings ⋮ A Wegner-type estimate for correlated potentials ⋮ Regularity of the density of states of random Schrödinger operators

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Kotani theory for one dimensional stochastic Jacobi matrices
• Almost periodic Schrödinger operators. II: The integrated density of states
• Remark on the continuity of the density of states of ergodic finite difference operators
• Supersymmetry and the Parisi-Sourlas dimensional reduction: a rigorous proof
• Subharmonicity of the Lyapunov index
• Harmonic analysis on SL(2,R) and smoothness of the density of states in the one-dimensional Anderson model
• Analyticity of the density of states and replica method for random Schrödinger operators on a lattice
• Some connections between excursion theory and the discrete Schrödinger equation with random potentials
• A supersymmetric transfer matrix and differentiability of the density of states in the one-dimensional Anderson model
• Spectral properties of disordered systems in the one-body approximation
• A rigorous replica trick approach to Anderson localization in one dimension
• Anderson localization for Bernoulli and other singular potentials
• On the density of states of Schrodinger operators with a random potential
• ON THE SPECTRUM OF THE ONE-DIMENSIONAL SCHRÖDINGER EQUATION WITH A RANDOM POTENTIAL