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Saddle points in the chaotic analytic function and Ginibre characteristic polynomial

By M.R. Dennis and J.H. Hannay

Abstract

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 pi^-1 |z|^-4 from the origin. <br/>This behaviour is expected to be general for finite or infinite polynomials with zeros uniformly randomly distributed in the complex plane, and which repel

Topics: QA, QC
Year: 2003
OAI identifier: oai:eprints.soton.ac.uk:29381
Provided by: e-Prints Soton

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Citations

  1. (2000). Universality and scaling between zeros on complex manifolds Invent.

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