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Lipschitz Continuity of the IDS

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1917)

In [306] Kotani and Simon extended to continuum alloy type models certain arguments previously used for the derivation of Wegner's estimate for the discrete Anderson model. They treated only the case where the single site potential is the characteristic function of the unit cube, but Combes and Hislop showed in [89] that the same argument extends to non-negative single site potentials with uniform lower bound on the unit cube. There also some steps of the proof have been streamlined.

Keywords

  • Unit Cube
  • Lipschitz Continuity
  • Toeplitz Matrix
  • Spectral Projection
  • Spectral Average

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© 2008 Springer-Verlag Berlin Heidelberg

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(2008). Lipschitz Continuity of the IDS. In: Existence and Regularity Properties of the Integrated Density of States of Random Schrödinger Operators. Lecture Notes in Mathematics, vol 1917. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72691-3_5

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