Large deviations for zeros of $P(\phi)_2$ random polynomials
Probability
2015-05-20 v1
Abstract
We extend results of Zeitouni-Zelditch on large deviations principles for zeros of Gaussian random polynomials in one complex variable to certain non-Gaussian ensembles that we call random polynomials. The probability measures are of the form where the actions are finite dimensional analgoues of those of quantum field theory. The speed and rate function are the same as in the associated Gaussian case. As a corollary, we prove that the expected distribution of zeros in the ensembles tends to the same equilibrium measure as in the Gaussian case.
Cite
@article{arxiv.1009.5142,
title = {Large deviations for zeros of $P(\phi)_2$ random polynomials},
author = {Renjie Feng and Steve Zelditch},
journal= {arXiv preprint arXiv:1009.5142},
year = {2015}
}
Comments
This is a continuation of the article Large deviations of empirical zero point measures on Riemann surfaces, I: $g = 0$ by O. Zeitouni, S. Zelditch (to appear in IMRN) and is not self-contained