Localization for discrete one-dimensional random word models

David Damanik, Roberts Sims, Günter Stolz

Research output: Contribution to journalArticle

8 Scopus citations

Abstract

We consider Schrödinger operators in ℓ2(ℤ) whose potentials are obtained by randomly concatenating words from an underlying set W according to some probability measure ν on W. Our assumptions allow us to consider models with local correlations, such as the random dimer model or, more generally, random polymer models, We prove spectral localization and, away from a finite set of exceptional energies, dynamical localization for such models. These results are obtained by employing scattering theoretic methods together with Furstenberg's theorem to verify the necessary input to perform a multiscale analysis.

Original languageEnglish (US)
Pages (from-to)423-445
Number of pages23
JournalJournal of Functional Analysis
Volume208
Issue number2
DOIs
StatePublished - Mar 15 2004
Externally publishedYes

Keywords

  • Anderson model
  • Localization
  • Random operators

ASJC Scopus subject areas

  • Analysis

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