On the joint distribution of energy levels of random Schrödinger operators

Michael Aizenman, Simone Warzel

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


We consider operators with random potentials on graphs, such as the lattice version of the random Schrödinger operator. The main result is a general bound on the probabilities of simultaneous occurrence of eigenvalues in specified distinct intervals, with the corresponding eigenfunctions being separately localized within prescribed regions. The bound generalizes the Wegner estimate on the density of states. The analysis proceeds through a new multi-parameter spectral averaging principle.

Original languageEnglish (US)
Article number045201
JournalJournal of Physics A: Mathematical and Theoretical
Issue number4
StatePublished - 2009

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modeling and Simulation
  • Mathematical Physics
  • General Physics and Astronomy


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