Hölder continuity of the integrated density of states in the one-dimensional Anderson model

Abstract

We consider the one-dimensional random Schrodinger operator H = H_0 + sigma V, where the potential V has i.i.d. entries with bounded support. We prove that the IDS is Holder continuous with exponent 1-c sigma This improves upon the work of Bourgain showing that the Holder exponent tends to 1 as sigma tends to 0 in the more specific Anderson-Bernoulli setting.

References in corpus (3)

• An Invitation to Random Schroedinger operators
• Dyson's spike for random Schroedinger operators and Novikov-Shubin invariants of groups
• On the Furstenberg measure and density of states for the Anderson-Bernoulli model at small disorder