Wegner estimates for sign-changing single site potentials

Abstract

We study Anderson and alloy type random Schrödinger operators on $\ell^2(\ZZ^d)$ and $L^2(\RR^d)$. Wegner estimates are bounds on the average number of eigenvalues in an energy interval of finite box restrictions of these types of operators. For a certain class of models we prove a Wegner estimate which is linear in the volume of the box and the length of the considered energy interval. The single site potential of the Anderson/alloy type model does not need to have fixed sign, but it needs be of a generalised step function form. The result implies the Lipschitz continuity of the integrated density of states.

References in corpus (4)

• Wegner estimate for discrete alloy-type models
• Spectral properties of discrete alloy-type models
• On the Lipschitz continuity of the integrated density of states for sign-indefinite potentials
• Lipschitz-continuity of the integrated density of states for Gaussian random potentials

Cited by in corpus (16)

• Wegner estimate for discrete alloy-type models
• Minami's estimate: beyond rank one perturbation and monotonicity
• Continuity of the integrated density of states on random length metric graphs
• Spectral properties of discrete alloy-type models
• Low lying eigenvalues of randomly curved quantum waveguides
• Low lying spectrum of weak-disorder quantum waveguides
• Wegner estimate and localization for alloy-type models with sign-changing exponentially decaying single-site potentials
• Level Spacing for Non-Monotone Anderson Models
• Decorrelation estimates for some continuous and discrete random schrödinger operators in dimension one and applications to spectral statistics
• Discrete alloy-type models: Regularity of distributions and recent results
• Universality of smoothness of Density of States in arbitrary higher-dimensional disorder under non-local interactions I. From Viéte--Euler identity to Anderson localization
• Some abstract Wegner estimates with applications
• Quantum Hamiltonians with weak random abstract perturbation. II. Localization in the expanded spectrum
• Localization for alloy-type models with non-monotone potentials
• Wegner estimate for discrete Schrödinger operators with Gaussian random potentials
• Spectra of Random Operators with absolutely continuous Integrated Density of States