Massive partition functions and complex eigenvalue correlations in Matrix Models with symplectic symmetry

Akemann G, Basile F (2007)
Nucl.Phys.B 766(1-3): 150-177.

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We compute all massive partition functions or characteristic polynomials andtheir complex eigenvalue correlation functions for non-Hermitean extensions ofthe symplectic and chiral symplectic ensemble of random matrices. Our resultsare valid for general weight functions without degeneracies of the massparameters. The expressions we derive are given in terms of the Pfaffian ofskew orthogonal polynomials in the complex plane and their kernel. They aremuch simpler than the corresponding expressions for symplectic matrix modelswith real eigenvalues, and we explicitly show how to recover these in theHermitean limit. This explains the appearance of three different kernels asquaternion matrix elements there in terms of derivatives of a single kernelhere. We compare to the Hermitean limit of complex matrix models with unitarysymmetry leading to some determinantal identities.
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Akemann G, Basile F. Massive partition functions and complex eigenvalue correlations in Matrix Models with symplectic symmetry. Nucl.Phys.B. 2007;766(1-3):150-177.
Akemann, G., & Basile, F. (2007). Massive partition functions and complex eigenvalue correlations in Matrix Models with symplectic symmetry. Nucl.Phys.B, 766(1-3), 150-177.
Akemann, G., and Basile, F. (2007). Massive partition functions and complex eigenvalue correlations in Matrix Models with symplectic symmetry. Nucl.Phys.B 766, 150-177.
Akemann, G., & Basile, F., 2007. Massive partition functions and complex eigenvalue correlations in Matrix Models with symplectic symmetry. Nucl.Phys.B, 766(1-3), p 150-177.
G. Akemann and F. Basile, “Massive partition functions and complex eigenvalue correlations in Matrix Models with symplectic symmetry”, Nucl.Phys.B, vol. 766, 2007, pp. 150-177.
Akemann, G., Basile, F.: Massive partition functions and complex eigenvalue correlations in Matrix Models with symplectic symmetry. Nucl.Phys.B. 766, 150-177 (2007).
Akemann, Gernot, and Basile, F. “Massive partition functions and complex eigenvalue correlations in Matrix Models with symplectic symmetry”. Nucl.Phys.B 766.1-3 (2007): 150-177.
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