H\"older continuity of the integrated density of states in the one-dimensional Anderson model

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.