Abstract
We consider the one-dimensional random Schrödinger operator
where the potential V has i.i.d. entries with bounded support. We prove that the IDS is Hölder continuous with exponent \({1-c \sigma}\). This improves upon the work of Bourgain showing that the Hölder exponent tends to 1 as sigma tends to 0 in the more specific Anderson–Bernoulli setting.
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Communicated by L. Erdös
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Hart, E., Virág, B. Hölder Continuity of the Integrated Density of States in the One-Dimensional Anderson Model. Commun. Math. Phys. 355, 839–863 (2017). https://doi.org/10.1007/s00220-017-2927-5
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DOI: https://doi.org/10.1007/s00220-017-2927-5