Correlations between zeros of a random polynomial
Mathematical Physics
2015-06-26 v2 Mesoscale and Nanoscale Physics
math.MP
Probability
Abstract
We obtain exact analytical expressions for correlations between real zeros of the Kac random polynomial. We show that the zeros in the interval are asymptotically independent of the zeros outside of this interval, and that the straightened zeros have the same limit translation invariant correlations. Then we calculate the correlations between the straightened zeros of the SO(2) random polynomial.
Cite
@article{arxiv.math-ph/0201012,
title = {Correlations between zeros of a random polynomial},
author = {Pavel Bleher and Xiaojun Di},
journal= {arXiv preprint arXiv:math-ph/0201012},
year = {2015}
}
Comments
31 pages, 2 figures; a revised version of the J. Stat. Phys. paper