Tau Functions and Matrix Integrals

Details Tau Functions and Matrix Integrals Tau Functions and Matrix Integrals

2002-10-07

arxiv.org/abs/math-ph/0210012v3

Physics

Mathematical Physics

Latex, 74 pages, no figures

Scientific paper

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.

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