Random matrix theory: Wigner-Dyson statistics and beyond. (Lecture notes of a course given at SISSA (Trieste, Italy))

Details Random matrix theory: Wigner-Dyson statistics and beyond. (Lecture notes of a course given at SISSA (Trieste, Italy)) Random matrix theory: Wigner-Dyson statistics and beyond. (Lecture notes of a course given at SISSA (Trieste, Italy))

2009-11-03

arxiv.org/abs/0911.0639v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

TeX, 27 pages

Scientific paper

This is a course on Random Matrix Theory which includes traditional as well as advanced topics presented with an extensive use of classical logarithmic plasma analogy and that of the quantum systems of one-dimensional interacting fermions with inverse square interaction (Calogero-Sutherland model). Certain non-invariant random matrix ensembles are also considered with the emphasis on the eigenfunction statistics in them. The course can also be viewed as introduction to theory of localization where the (non-invariant) random matrix ensembles play a role of the toy models to illustrate functional methods based on super-vector/super-matrix representations.

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