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Continuity of integrated density of states — independent randomness

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In this paper we discuss the continuity properties of the integrated density of states for random models based on that of the single site distribution. Our results are valid for models with independent randomness with arbitrary free parts. In particular in the case of the Anderson type models (with stationary, growing, decaying randomness) on the ν dimensional lattice, with or without periodic and almost periodic backgrounds, we show that if the single site distribution is uniformly α-Hölder continuous, 0 < α ≤ 1, then the density of states is also uniformly α-Hölder continuous.

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  1. Institute for Mathematical Sciences, Taramani, Chennai, 600 113, India

    M. Krishna

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  1. M. Krishna
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Correspondence to M. Krishna.

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Dedicated to Michael Demuth on his 60th birthday

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Krishna, M. Continuity of integrated density of states — independent randomness. Proc Math Sci 117, 401–410 (2007). https://doi.org/10.1007/s12044-007-0034-9

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  • DOI: https://doi.org/10.1007/s12044-007-0034-9

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