We compute the correlation functions mixing the powers of two non-commuting random matrices within the same trace. The angular part of the integration was partially known in the literature (Morozov A 1992 Mod. Phys. Lett. A 7 3503, Shatashvili S L 1993 Commun. Math. Phys. 154 421): we pursue the calculation and carry out the eigenvalue integration reducing the problem to the construction of the associated bi-orthogonal polynomials. The generating function of these correlations then becomes a determinant involving the recursion coefficients of the bi-orthogonal polynomials.

Mixed correlation functions of the two-matrix model / Bertola, M.; Eynard, B.. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND GENERAL. - ISSN 0305-4470. - 36:28(2003), pp. 7733-7750. [10.1088/0305-4470/36/28/304]

Mixed correlation functions of the two-matrix model

Bertola, M.;
2003-01-01

Abstract

We compute the correlation functions mixing the powers of two non-commuting random matrices within the same trace. The angular part of the integration was partially known in the literature (Morozov A 1992 Mod. Phys. Lett. A 7 3503, Shatashvili S L 1993 Commun. Math. Phys. 154 421): we pursue the calculation and carry out the eigenvalue integration reducing the problem to the construction of the associated bi-orthogonal polynomials. The generating function of these correlations then becomes a determinant involving the recursion coefficients of the bi-orthogonal polynomials.
2003
36
28
7733
7750
https://iopscience.iop.org/article/10.1088/0305-4470/36/28/304/meta
https://arxiv.org/abs/hep-th/0303161
Bertola, M.; Eynard, B.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/14771
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