In this paper we find the asymptotic main term of the variance of the number of roots of Kostlan-Shub-Smale random polynomials and prove a central limit theorem for the number of roots as the degree goes to infinity.
@article{arxiv.1504.05355,
title = {CLT for the zeros of Kostlan Shub Smale random polynomials},
author = {Federico Dalmao},
journal= {arXiv preprint arXiv:1504.05355},
year = {2015}
}