Loop equation analysis of the circular β ensembles

@article{Witte2015LoopEA,
  title={Loop equation analysis of the circular β ensembles},
  author={Nicholas S. Witte and Peter J. Forrester},
  journal={Journal of High Energy Physics},
  year={2015},
  volume={2015},
  pages={1-42}
}
  • Nicholas S. Witte, Peter J. Forrester
  • Published 2015
  • Physics, Mathematics
  • Journal of High Energy Physics
  • A bstractWe construct a hierarchy of loop equations for invariant circular ensembles. These are valid for general classes of potentials and for arbitrary inverse temperatures Re β > 0 and number of eigenvalues N. Using matching arguments for the resolvent functions of linear statistics f(ζ) = (ζ + z)/(ζ − z) in a particular asymptotic regime, the global regime, we systematically develop the corresponding large N expansion and apply this solution scheme to the Dyson circular ensemble. Currently… CONTINUE READING

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    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 40 REFERENCES

    Random Matrices, volume 142 of Pure and Applied Mathematics (Amsterdam)

    • M. L. Mehta
    • 2004
    VIEW 10 EXCERPTS
    HIGHLY INFLUENTIAL

    Statistical theory of the energy levels of complex systems. I

    VIEW 22 EXCERPTS
    HIGHLY INFLUENTIAL

    Unitary matrix models and phase transition

    VIEW 5 EXCERPTS
    HIGHLY INFLUENTIAL

    UNITARY MATRIX MODELS AND PAINLEVÉ III

    VIEW 5 EXCERPTS
    HIGHLY INFLUENTIAL

    The uses of the refined matrix model recursion

    VIEW 4 EXCERPTS
    HIGHLY INFLUENTIAL