Course:
Random Matrices
by Vladimir Kravtsov
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
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