Symmetry classes in random matrix theory

Abstract

Dyson's (1962) classification of matrix ensembles is reviewed from a modern perspective, and its recent extension to disordered fermion problems is motivated and described. It is explained in particular why symmetry classes are associated with large families of symmetric spaces.

Short review article (max. 4000 words) solicited by the editors of the Encylopedia of Mathematical Physics (Elsevier, 2005)

References in corpus (1)

• The spectrum of the QCD Dirac operator and chiral random matrix theory: the threefold way

Cited by in corpus (4)

• Introduction to Random Matrices - Theory and Practice
• A conjecture on Hubbard-Stratonovich transformations for the Pruisken-Schäfer parameterisations of real hyperbolic domains
• Large deviations for the largest eigenvalue of disordered bosons and disordered fermionic systems
• Quantum Chaos, Randomness and Universal Scaling of Entanglement in Various Krylov Spaces