Mixed Correlation Functions of the Two-Matrix Model

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: we pursue the calculation and carry out the eigenvalue integration reducing the problem to the construction of the associated biorthogonal polynomials. The generating function of these correlations becomes then a determinant involving the recursion coefficients of the biorthogonal polynomials.

16 pages

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Cited by in corpus (13)

• Unitary Integrals and Related Matrix Models
• A new Chiral Two-Matrix Theory for Dirac Spectra with Imaginary Chemical Potential
• Free Energy of the Two-Matrix Model/dToda Tau-Function
• Chern-Simons Theory, 2d Yang-Mills, and Lie Algebra Wanderers
• Mixed correlation functions in the 2-matrix model, and the Bethe ansatz
• 2-matrix versus complex matrix model, integrals over the unitary group as triangular integrals
• Mixed correlation function and spectral curve for the 2-matrix model
• Second and Third Order Observables of the Two-Matrix Model
• A short note about Morozov's formula
• Scattering of Long Folded Strings and Mixed Correlators in the Two-Matrix Model
• Long Strings and Chiral Non-Singlets in Matrix Quantum Mechanics
• Two-matrix model with semiclassical potentials and extended Whitham hierarchy
• One-matrix differential reformulation of two-matrix models