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Please use this identifier to cite or link to this item: http://bura.brunel.ac.uk/handle/2438/445

Title: Massive partition functions and complex eigenvalue correlations in Matrix Models with symplectic symmetry
Authors: Akemann, G
Basile, F
Keywords: Mathematical physics
Publication Date: 2006
Publisher: Elsevier
Citation: Nuclear physics B 766: 150-177, Jun 2006
Abstract: We compute all massive partition functions or characteristic polynomials and their complex eigenvalue correlation functions for non-Hermitean extensions of the symplectic and chiral symplectic ensemble of random matrices. Our results are valid for general weight functions without degeneracies of the mass parameters. The expressions we derive are given in terms of the Pfaffian of skew orthogonal polynomials in the complex plane and their kernel. They are much simpler than the corresponding expressions for symplectic matrix models with real eigenvalues, and we explicitly show how to recover these in the Hermitean limit. This explains the appearance of three different kernels as quaternion matrix elements there in terms of derivatives of a single kernel here. We compare to the Hermitean limit of complex matrix models with unitary symmetry leading to some determinantal identities.
URI: http://bura.brunel.ac.uk/handle/2438/445
DOI: http://dx.doi.org/10.1016/j.nuclphysb.2006.12.008
Appears in Collections:Mathematical Science
Dept of Mathematics Research Papers

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