Non-Lifshitz Tails at the Spectral Bottom of Some Random Operators |
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Authors: | Hatem Najar |
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Institution: | (1) Département de Mathématiques, I.S.M.A.I. Kairouan, Bd Assad Ibn Elfourat, 3100 Kairouan, Tunisia |
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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
. Being periodic,
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.
Research partially supported by the Research Unity 01/UR/ 15-01 projects. |
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Keywords: | Spectral theory Random operators Integrated density of states Lifshitz tails |
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