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We give a closed form for the correlation functions of ensembles of a class of asymmetric real matrices in terms of the Pfaffian of an antisymmetric matrix formed from a $2 \times 2$ matrix kernel associated to the ensemble.
On some multiple integrals involving determinants
N. G. de Bruijn · 1955
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Statistical ensembles of complex, quaternion, and real matrices
Jean Ginibre · 1965
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Uniform asymptotic expansions of the incomplete gamma functions and the incomplete beta function
N. M. Temme · 1975
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V. L. Girko · 1984
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Nonintersecting paths, Pfaffians, and plane partitions
John R. Stembridge · 1990
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Asymptotics for the zeros of the partial sums of e z e^{z} . I
A. J. Carpenter, R. S. Varga, and J. Waldvogel · 1991
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N. Lehmann and H.-J. Sommers · 1991
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Alan Edelman, Eric Kostlan, and Michael Shub · 1994
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Z. D. Bai · 1997
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Statistics of real eigenvalues in Ginibre’s ensemble of random real matrices
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Integrable structure of Ginibre’s ensemble of real random matrices and a pfaffian integration theorem, 2007
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Eigenvalue statistics of the real Ginibre ensemble
Peter J. Forrester and Taro Nagao · 2007
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Averages over Ginibre’s ensemble of random real matrices
Christopher D Sinclair · 2007
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Shey-Jey Chern and Jeffrey D. Vaaler · 2001
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Random matrices close to Hermitian or unitary: overview of methods and results
Yan V. Fyodorov and H.-J. Sommers · 2003
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Madan Lal Mehta · 2004
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Skew orthogonal polynomials and the partly symmetric real Ginibre ensemble
Peter Forrester and Taro Nagao
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Random Matrices: The circular Law
T. Tao and V. Vu · 2007
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The range of multiplicative functions on ℂ [ x ] , ℝ [ x ] \mathbb{C}[x],\mathbb{R}[x] and ℤ [ x ] \mathbb{Z}[x]
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