Random Matrices

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random matrix


Random matrix theory and its application to Anderson localization and
mesoscopic systems.

Main Topics

Wigner-Dyson random matrix theory

  • Dyson universality classes
  • eigenvalue statistics
  • eigenfunction statistics
  • crossover between universality classes
  • description in terms of orthogonal polynomilas and nonlinear
    supersymmetric sigma model

Physics of quantum dots and Winger-Dyson random matrix theory

  • statistics of conductances
  • weak localization and magnetoresistance

Anderson localization and the relevant random matrix ensembles

  • banded random matrices
  • random matrices with multifractal eigenfunctions
  • critical random matrix ensemble

Lecture Notes

Lecture notes are available as an arXiv pre-print.

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