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Borel summability in the disorder parameter of the averaged Green's function for Gaussian disorder

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Abstract

In this note we prove Borel summability in the disorder parameter of the averaged Green's function <G(E,x,y>) y of tight binding models

$$H_V = - \Delta + V$$

with Gaussian disorder

$$d\lambda (V) = (2\pi \gamma )^{ - 1/2} \exp ( - V^2 /2\gamma )dV$$

forγ→0 and fixed large |E|. Using this, we can reconstruct the density of states ϱ(E)γ from the Borel sums of <G(E,x,x>) y with ImE↗0 and ImE↘0.

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Authors and Affiliations

  1. Institut für Angewandte Mathematik, Universität Frankfurt am Main, D-6000, Frankfurt, Federal Republic of Germany

    F. Constantinescu, K. Klöckner & U. Scharffenberger

Authors
  1. F. Constantinescu
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  2. K. Klöckner
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  3. U. Scharffenberger
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Communicated by T. Spencer

Supported in part by the Deutsche Forschungsgemeinschaft

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Constantinescu, F., Klöckner, K. & Scharffenberger, U. Borel summability in the disorder parameter of the averaged Green's function for Gaussian disorder. Commun.Math. Phys. 98, 203–211 (1985). https://doi.org/10.1007/BF01220508

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  • DOI: https://doi.org/10.1007/BF01220508

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