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Title: Statistics of real eigenvalues in Ginibre's Ensemble of random real matrices
Authors: Kanzieper, E
Akemann, G
Keywords: Mathematical physics;Disordered systems and neural networks;Exactly solvable and integrable systems
Issue Date: 2005
Publisher: The American Physical Society
Citation: Physical Review Letters 95, Article no: 230201, Nov 2005
Abstract: The integrable structure of Ginibre's orthogonal ensemble of random matrices is looked at through the prism of the probability pn,k to find exactly k real eigenvalues in the spectrum of an n×n real asymmetric Gaussian random matrix. The exact solution for the probability function pn,k is presented, and its remarkable connection to the theory of symmetric functions is revealed. An extension of the Dyson integration theorem is a key ingredient of the theory presented.
Appears in Collections:Dept of Mathematics Research Papers
Mathematical Sciences

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