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Letters in Mathematical Physics

, Volume 34, Issue 2, pp 103–117 | Cite as

Localization for random potentials supported on a subspace

  • V. Grinshpun
Article

Abstract

We consider the lattice Schrödinger operator acting onl2 (ℤ d ) with random potential (independent, identically distributed random variables), supported on a subspace of dimension 1 ⩽v <d. We use the multiscale analyses scheme to prove that this operator exhibits exponential localization at the edges of the spectrum for any disorder or outside the interval [-2d, 2d] for sufficiently high disorder.

Mathematics Subject Classifications (1991)

47N55 82Bxx 60H25 82D35 

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Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • V. Grinshpun
    • 1
  1. 1.Institut de Mathématiques de Paris-Jussieu, UMR C9994Physique mathématique et Géométrie, Université Paris 7 Denis DiderotParis Cedex 05France

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