Statistics of Real Eigenvalues in Ginibre's Ensemble of Random Real Matrices

Kanzieper E, Akemann G (2005)
Phys.Rev.Lett. 95(23).

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The integrable structure of Ginibre's Orthogonal Ensemble of random matricesis looked at through the prism of the probability "p_{n,k}" to find exactly "k"real eigenvalues in the spectrum of an "n" by "n" real asymmetric Gaussianrandom matrix. The exact solution for the probability function "p_{n,k}" ispresented, and its remarkable connection to the theory of symmetric functionsis revealed. An extension of the Dyson integration theorem is a key ingredientof the theory presented.
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Kanzieper E, Akemann G. Statistics of Real Eigenvalues in Ginibre's Ensemble of Random Real Matrices. Phys.Rev.Lett. 2005;95(23).
Kanzieper, E., & Akemann, G. (2005). Statistics of Real Eigenvalues in Ginibre's Ensemble of Random Real Matrices. Phys.Rev.Lett., 95(23).
Kanzieper, E., and Akemann, G. (2005). Statistics of Real Eigenvalues in Ginibre's Ensemble of Random Real Matrices. Phys.Rev.Lett. 95.
Kanzieper, E., & Akemann, G., 2005. Statistics of Real Eigenvalues in Ginibre's Ensemble of Random Real Matrices. Phys.Rev.Lett., 95(23).
E. Kanzieper and G. Akemann, “Statistics of Real Eigenvalues in Ginibre's Ensemble of Random Real Matrices”, Phys.Rev.Lett., vol. 95, 2005.
Kanzieper, E., Akemann, G.: Statistics of Real Eigenvalues in Ginibre's Ensemble of Random Real Matrices. Phys.Rev.Lett. 95, (2005).
Kanzieper, Eugene, and Akemann, Gernot. “Statistics of Real Eigenvalues in Ginibre's Ensemble of Random Real Matrices”. Phys.Rev.Lett. 95.23 (2005).
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