Skew-orthogonal Laguerre polynomials for chiral real asymmetric random matrices

@article{Akemann2010SkeworthogonalLP,
  title={Skew-orthogonal Laguerre polynomials for chiral real asymmetric random matrices},
  author={G. Akemann and M. Kieburg and M. Phillips},
  journal={Journal of Physics A},
  year={2010},
  volume={43},
  pages={375207}
}
  • G. Akemann, M. Kieburg, M. Phillips
  • Published 2010
  • Mathematics, Physics
  • Journal of Physics A
  • We apply the method of skew-orthogonal polynomials (SOP) in the complex plane to asymmetric random matrices with real elements, belonging to two different classes. Explicit integral representations valid for arbitrary weight functions are derived for the SOP and for their Cauchy transforms, given as the expectation values of traces and determinants or their inverses, respectively. Our proof uses the fact that the joint probability distribution function for all combinations of real eigenvalues… CONTINUE READING
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