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Hölder Equicontinuity of the Integrated Density of States at Weak Disorder

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Abstract

Hölder continuity, |Nλ(E)−Nλ(E’)|≤ C |E − E′|α, with a constant C independent of the disorder strength λ is proved for the integrated density of states Nλ(E) associated to a discrete random operator H=H o + λ V consisting of a translation invariant hopping matrix H o and i.i.d. single site potentials V with an absolutely continuous distribution, under a regularity assumption for the hopping term.

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Authors and Affiliations

  1. Institut für Theoretische Physik, ETH, Zürich, CH-8093, Zürich, Switzerland

    Jeffrey H. Schenker

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  1. Jeffrey H. Schenker
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Correspondence to Jeffrey H. Schenker.

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Mathematics Subject Classifications (2000). 82D30, 46N55, 47N55.

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Schenker, J.H. Hölder Equicontinuity of the Integrated Density of States at Weak Disorder. Lett Math Phys 70, 195–209 (2004). https://doi.org/10.1007/s11005-004-3757-x

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  • DOI: https://doi.org/10.1007/s11005-004-3757-x

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