Saddle points in the chaotic analytic function and Ginibre characteristic polynomial

@article{Dennis2003SaddlePI,
  title={Saddle points in the chaotic analytic function and Ginibre characteristic polynomial},
  author={Mark R. Dennis and J. H. Hannay},
  journal={Journal of Physics A},
  year={2003},
  volume={36},
  pages={3379-3383}
}
Comparison is made between the distribution of saddle points in the chaotic analytic function and in the characteristic polynomials of the Ginibre ensemble. Realizing the logarithmic derivative of these infinite polynomials as the electric field of a distribution of Coulombic charges at the zeros, a simple mean-field electrostatic argument shows that the density of saddles minus zeros falls off as π−1 |z|−4 from the origin. This behaviour is expected to be general for finite or infinite… 

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