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Tau Functions and Matrix Integrals
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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.
Forward citations
Cited by 2 Pith papers
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Superintegrability for some $(q,t)$-deformed matrix models
Proves uniqueness of solutions to constraints on (q,t)-deformed hypergeometric functions and derives superintegrability relations for a general (q,t)-deformed matrix model with allowed parameters.
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The generalized Wronskian solutions of the constrained mKP hierarchy
Generalized Wronskian solutions, encompassing Wronskians and Grammians, are shown to satisfy the bilinear equations of the (k,m)-constrained mKP hierarchy.
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