Skew-orthogonal Laguerre polynomials for chiral real asymmetric random matrices

@inproceedings{Akemann2010SkeworthogonalLP,
  title={Skew-orthogonal Laguerre polynomials for chiral real asymmetric random matrices},
  author={Gernot Akemann and Mario Kieburg and Michael J. Phillips},
  year={2010}
}
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

Citations

Publications citing this paper.
SHOWING 1-10 OF 12 CITATIONS

A geometrical triumvirate of real random matrices

VIEW 4 EXCERPTS
CITES BACKGROUND & METHODS
HIGHLY INFLUENCED

References

Publications referenced by this paper.
SHOWING 1-10 OF 27 REFERENCES

Nucl

G. Akemann, F. Basile
  • Phys. B766
  • 2007
VIEW 16 EXCERPTS
HIGHLY INFLUENTIAL

J

G. Akemann, A. Pottier
  • Phys., A37
  • 2004
VIEW 39 EXCERPTS
HIGHLY INFLUENTIAL

Int

P. Di Francesco, M. Gaudin, C. Itzykson, F. Lesage
  • J. Mod. Phys. A9
  • 1994
VIEW 16 EXCERPTS
HIGHLY INFLUENTIAL

Phys

P. J. Forrester, A. Mays, J. Stat
  • 134
  • 2009
VIEW 17 EXCERPTS
HIGHLY INFLUENTIAL

Random Matrices

M. L. Mehta
  • Academic Press, Third Edition, London
  • 2004
VIEW 4 EXCERPTS
HIGHLY INFLUENTIAL

J

M. Kieburg, T. Guhr
  • Phys. A43
  • 2010

J

G. Akemann, M. J. Phillips, H.-J. Sommers
  • Phys. A43
  • 2010