Autocorrelation of Random Matrix Polynomials

@article{Conrey2003AutocorrelationOR,
  title={Autocorrelation of Random Matrix Polynomials},
  author={J. Brian Conrey and David W. Farmer and Jonathan P. Keating and Michael O. Rubinstein and Nina C. Snaith},
  journal={Communications in Mathematical Physics},
  year={2003},
  volume={237},
  pages={365-395}
}
Abstract: We calculate the autocorrelation functions (or shifted moments) of the characteristic polynomials of matrices drawn uniformly with respect to Haar measure from the groups U(N), O(2N) and USp(2N). In each case the result can be expressed in three equivalent forms: as a determinant sum (and hence in terms of symmetric polynomials), as a combinatorial sum, and as a multiple contour integral. These formulae are analogous to those previously obtained for the Gaussian ensembles of Random… 
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