An eigensystem approach to Anderson localization

Alexander Elgart, Abel Klein

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


We introduce a new approach for proving localization (pure point spectrum with exponentially decaying eigenfunctions, dynamical localization) for the Anderson model at high disorder. In contrast to the usual strategy, we do not study finite volume Green's functions. Instead, we perform a multiscale analysis based on finite volume eigensystems (eigenvalues and eigenfunctions). Information about eigensystems at a given scale is used to derive information about eigensystems at larger scales. This eigensystem multiscale analysis treats all energies of the finite volume operator at the same time, establishing level spacing and localization of eigenfunctions in a fixed box with high probability. A new feature is the labeling of the eigenvalues and eigenfunctions by the sites of the box.

Original languageEnglish
Pages (from-to)3465-3512
Number of pages48
JournalJournal of Functional Analysis
Issue number12
StatePublished - 15 Dec 2016
Externally publishedYes


  • Anderson localization
  • Anderson model
  • Hall's Marriage Theorem
  • Level spacing
  • Multiscale analysis
  • Random Schrödinger operators

ASJC Scopus subject areas

  • Analysis


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