Saddle points in the chaotic analytic function and Ginibre characteristic polynomial

Details Saddle points in the chaotic analytic function and Ginibre characteristic polynomial Saddle points in the chaotic analytic function and Ginibre characteristic polynomial

2002-09-26

arxiv.org/abs/nlin/0209056v3

Nonlinear Sciences

Chaotic Dynamics

6 pages, 2 figures; revised

Scientific paper

10.1088/0305-4470/36/12/329

Comparison is made between the distribution of saddle points in the chaotic analytic function and in the characteristic polynomials of the Ginibre ensemble. Realising 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. This behaviour is expected to be general for finite or infinite polynomials with zeros uniformly randomly distributed in the complex plane, and which repel quadratically.

Affiliated with

Also associated with

No associations

Rating

Saddle points in the chaotic analytic function and Ginibre characteristic polynomial does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Saddle points in the chaotic analytic function and Ginibre characteristic polynomial, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Saddle points in the chaotic analytic function and Ginibre characteristic polynomial will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-524105