Tau Functions and Matrix Integrals

Abstract

We consider solvable matrix models. We generalize Harish-Chandra-Itzykson-Zuber and certain other integrals (Gross-Witten integral and integrals over complex matrices) using the notion of tau function of matrix argument. In this case one can reduce the matrix integral to the integral over eigenvalues, which in turn is certain tau function. The resulting tau function may be analyzed either by the method of orthogonal polynomials or by the Schur functions expansion method.

Latex, 74 pages, no figures

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Cited by in corpus (9)

• Complex matrix model duality
• Fermionic construction of tau functions and random processes
• Classical group matrix models and universal criticality
• On permanental polynomials of certain random matrices
• Unitary matrix integrals, symmetric polynomials, and long-range random walks
• Diagonal Solutions to the 2-Toda Hierarchy
• One-matrix differential reformulation of two-matrix models
• Comments on Slavnov products, Temperley-Lieb open spin chains, and KP tau functions
• Character expansion of matrix integrals