English

Exact statistics of complex zeros for Gaussian random polynomials with real coefficients

chao-dyn 2009-10-28 v1 Chaotic Dynamics

Abstract

k-point correlations of complex zeros for Gaussian ensembles of Random Polynomials of order N with Real Coefficients (GRPRC) are calculated exactly, following an approach of Hannay for the case of Gaussian Random Polynomials with Complex Coefficients (GRPCC). It is shown that in the thermodynamic limit NN \to \infty of Gaussian random holomorphic functions all the statistics converge to the their GRPCC counterparts as one moves off the real axis, while close to the real axis the two cases are essentially different. Special emphasis is given to 1 and 2 point correlation functions in various regimes.

Cite

@article{arxiv.chao-dyn/9612005,
  title  = {Exact statistics of complex zeros for Gaussian random polynomials with real coefficients},
  author = {Tomaz Prosen},
  journal= {arXiv preprint arXiv:chao-dyn/9612005},
  year   = {2009}
}

Comments

8 pages in plain Latex (3 figures available upon request)

R2 v1 2026-07-22T09:55:29.476Z