Nonlinear random matrix statistics, symmetric functions and hyperdeterminants

@article{Luque2010NonlinearRM,
  title={Nonlinear random matrix statistics, symmetric functions and hyperdeterminants},
  author={J. Luque and P. Vivo},
  journal={Journal of Physics A},
  year={2010},
  volume={43},
  pages={085213}
}
  • J. Luque, P. Vivo
  • Published 2010
  • Physics, Mathematics
  • Journal of Physics A
  • Nonlinear statistics (i.e. statistics of permanents) on the eigenvalues of invariant random matrix models are considered for the three Dyson's symmetry classes β = 1, 2, 4. General formulas in terms of hyperdeterminants are found for β = 2. For specific cases and all βs, more computationally efficient results are obtained, based on symmetric functions expansions. As an application, we consider the case of quantum transport in chaotic cavities extending results from Savin et al (2008 Phys. Rev… CONTINUE READING
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    SHOWING 1-10 OF 96 REFERENCES
    Statistics of real eigenvalues in Ginibre's ensemble of random real matrices.
    • 44
    • PDF
    Quantum conductance problems and the Jacobi ensemble
    • 63
    • PDF
    On permanental polynomials of certain random matrices
    • 7
    • PDF
    Fluctuation formula for complex random matrices
    • 27
    • PDF
    Random-matrix theory of mesoscopic fluctuations in conductors and superconductors.
    • Beenakker
    • Physics, Medicine
    • Physical review. B, Condensed matter
    • 1993
    • 34
    • PDF
    Integrable theory of quantum transport in chaotic cavities.
    • 34
    • PDF