A lower bound for the density of states of the lattice Anderson model

DOI10.1090/S0002-9939-08-09361-1zbMath1143.47027arXiv0705.1707MaRDI QIDQ3518248

Peter Müller, Peter D. Hislop

Publication date: 7 August 2008

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0705.1707

zbMATH Keywords

random Schrödinger operatorsintegrated density of stateslower boundWegner estimate

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Random linear operators (47B80)

Related Items (8)

Renormalization group analysis of the hierarchical Anderson model ⋮ An application of singular traces to crystals and percolation ⋮ On the regime of localized excitations for disordered oscillator systems ⋮ Concentration of eigenvalues for skew-shift Schrödinger operators ⋮ Random block operators ⋮ Minami's estimate: beyond rank one perturbation and monotonicity ⋮ The spectral shift function for compactly supported perturbations of Schrödinger operators on large bounded domains ⋮ A lower Wegner estimate and bounds on the spectral shift function for continuum random Schrödinger operators

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Spectral properties of the Laplacian on bond-percolation graphs
• Localization at large disorder and at extreme energies: an elementary derivation
• Localization for some continuous, random Hamiltonians in \(d\)-dimensions
• Existence of the density of states for multi-dimensional continuum Schrödinger operators with Gaussian random potentials
• The stability of the density of states of Schrödinger operator under very small perturbations
• Local fluctuation of the spectrum of a multidimensional Anderson tight binding model
• An optimal Wegner estimate and its application to the global continuity of the integrated density of states for random Schrödinger operators
• Small Perturbations and the Eigenvalues of the Laplacian on Large Bounded Domains
• The absolute continuity of the integrated density of states for magnetic Schrödinger operators with certain unbounded random potentials

This page was built for publication: A lower bound for the density of states of the lattice Anderson model