On the Lipschitz continuity of the integrated density of states for sign-indefinite potentials

Abstract

The present paper is devoted to the study of spectral properties of random Schroedinger operators. Using a finite section method for Toeplitz matrices, we prove a Wegner estimate for some alloy type models where the single site potential is allowed to change sign. The results apply to the corresponding discrete model, too. In certain disorder regimes we are able to prove the Lipschitz continuity of the integrated density of states and/or localization near spectral edges.

arXiv commentUses epic and eepic styles

References in corpus (4)

• The absolute continuity of the integrated density of states for magnetic Schrödinger operators with certain unbounded random potentials
• Regularity of the Density of Surface States
• Localization for random perturbations of periodic Schroedinger operators with regular Floquet eigenvalues
• Wegner estimate and the density of states of some indefinite alloy type Schroedinger Operators

Cited by in corpus (12)

• Anderson localization for a class of models with a sign-indefinite single-site potential via fractional moment method
• Wegner estimate for discrete alloy-type models
• Wegner estimates for sign-changing single site potentials
• Continuity of the integrated density of states on random length metric graphs
• Continuity properties of the integrated density of states on manifolds
• Localization via fractional moments for models on $\mathbb{Z}$ with single-site potentials of finite support
• 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
• Quantum Hamiltonians with weak random abstract perturbation. I. Initial length scale estimate
• Quantum Hamiltonians with weak random abstract perturbation. II. Localization in the expanded spectrum
• Wegner estimate for discrete Schrödinger operators with Gaussian random potentials