Localization for discrete one-dimensional random word models

David Damanik, Robert J Sims, Günter Stolz

Research output: Contribution to journalArticle

7 Citations (Scopus)

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

Fingerprint

Multiscale Analysis
Dimer
Model
Probability Measure
Finite Set
Polymers
Scattering
Verify
Necessary
Operator
Energy
Theorem

Keywords

  • Anderson model
  • Localization
  • Random operators

ASJC Scopus subject areas

  • Analysis

Cite this

Localization for discrete one-dimensional random word models. / Damanik, David; Sims, Robert J; Stolz, Günter.

In: Journal of Functional Analysis, Vol. 208, No. 2, 15.03.2004, p. 423-445.

Research output: Contribution to journalArticle

Damanik, David ; Sims, Robert J ; Stolz, Günter. / Localization for discrete one-dimensional random word models. In: Journal of Functional Analysis. 2004 ; Vol. 208, No. 2. pp. 423-445.
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