Spectral averaging, perturbation of singular spectra, and localization

J. M. Combes, P. D. Hislop, E. Mourre

Research output: Contribution to journalArticlepeer-review

37 Scopus citations


A spectral averaging theorem is proved for one-parameter families of self-adjoint operators using the method of differential inequalities. This theorem is used to establish the absolute continuity of the averaged spectral measure with respect to Lebesgue measure. This is an important step in controlling the singular continuous spectrum of the family for almost all values of the parameter. The main application is to the problem of localization for certain families of random Schrödinger operators. Localization for a family of random Schrödinger operators is established employing these results and a multi-scale analysis.

Original languageEnglish
Pages (from-to)4883-4894
Number of pages12
JournalTransactions of the American Mathematical Society
Issue number12
StatePublished - 1996

ASJC Scopus subject areas

  • Mathematics (all)
  • Applied Mathematics


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