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A note on the Pfaffian integration theorem

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Alexei Borodin1 and Eugene Kanzieper2

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Akemann G and Kanzieper E 2007 Integrable structure of Ginibre's ensemble of real random matrices and a Pfaffian integration theorem Preprint math-ph/0703019 (J. Stat. Phys. submitted)
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Ginibre J 1965 Statistical ensembles of complex, quaternion, and real matrices J. Math. Phys. 19 133

 
Ishikawa M and Wakayama M 1995 Minor summation formula of Pfaffians Linear Multilinear Algebra 39 285
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Ishikawa M and Wakayama M 2000 Minor summation formulas of Pfaffians, survey and a new identity Adv. Stud. Pure Math. 28 133

 
Kanzieper E and Akemann G 2005 Statistics of real eigenvalues in Ginibre's ensemble of random real matrices Phys. Rev. Lett. 95 230201
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Macdonald I G 1998 Symmetric Functions and Hall Polynomials (Oxford: Oxford University Press)

 
Mahoux G and Mehta M L 1991 A method of integration over matrix variables J. Phys. I (France) 1 1093
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Rains E M 2000 Correlation functions for symmetrized increasing subsequences Preprint math.CO/0006097
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Tracy C A and Widom H 1998 Correlation functions, cluster functions and spacing distributions for random matrices J. Stat. Phys. 92 809
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