General eigenvalue correlations for the real Ginibre ensemble

@inproceedings{Sommers2008GeneralEC,
  title={General eigenvalue correlations for the real Ginibre ensemble},
  author={Hans Dipl Ing Sommers and Waldemar Wieczorek},
  year={2008}
}
We rederive in a simplified version the Lehmann-Sommers eigenvalue distribution for the Gaussian ensemble of asymmetric real matrices, invariant under real orthogonal transformations, as a basis for a detailed derivation of a Pfaffian generating functional for n-point densities. This produces a simple free-fermion diagram expansion for the correlations leading to quaternion determinants in each order n. All will explicitly be given with the help of a very simple symplectic kernel for even… CONTINUE READING

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  • H.-J. Sommers, J. Phys
  • 671
  • 2007
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