Universal correlations in random matrices: quantum chaos, the $1/r^2$ integrable model, and quantum gravity

Details Universal correlations in random matrices: quantum chaos, the $1/r^2$ integrable model, and quantum gravity Universal correlations in random matrices: quantum chaos, the $1/r^2$ integrable model, and quantum gravity

1996-12-26

arxiv.org/abs/hep-th/9612242v1

Mod.Phys.Lett. A11 (1996) 1201

Physics

High Energy Physics

High Energy Physics - Theory

26 pages, LaTex

Scientific paper

10.1142/S0217732396001223

Random matrix theory (RMT) provides a common mathematical formulation of distinct physical questions in three different areas: quantum chaos, the 1-d integrable model with the $1/r^2$ interaction (the Calogero-Sutherland-Moser system), and 2-d quantum gravity. We review the connection of RMT with these areas. We also discuss the method of loop equations for determining correlation functions in RMT, and smoothed global eigenvalue correlators in the 2-matrix model for gaussian orthogonal, unitary and symplectic ensembles.

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