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Non-Lifshitz Tails at the Spectral Bottom of Some Random Operators

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Abstract

In this paper we continue with the investigation of the behavior of the integrated density of states of random operators of the form H ω =−∇ ρ ω ∇. In the present work we are interested in its behavior at 0, the bottom of the spectrum of H ω . We prove that it converges exponentially fast to the integrated density of states of some periodic operator  \(\overline{H}\) . Being periodic, \(\overline{H}\) cannot exhibit a Lifshitz behaviour. This result relates to the result of S.M. Kozlov (Russ. Math. Surv. 34(4):168–169, 1979) and improves it.

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  1. Département de Mathématiques, I.S.M.A.I. Kairouan, Bd Assad Ibn Elfourat, 3100, Kairouan, Tunisia

    Hatem Najar

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  1. Hatem Najar
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Correspondence to Hatem Najar.

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Research partially supported by the Research Unity 01/UR/ 15-01 projects.

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Najar, H. Non-Lifshitz Tails at the Spectral Bottom of Some Random Operators. J Stat Phys 130, 713–725 (2008). https://doi.org/10.1007/s10955-007-9467-x

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  • DOI: https://doi.org/10.1007/s10955-007-9467-x

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