Concentration inequalities for the number of real zeros of Kac polynomials
We study concentration inequalities for the number of real roots of the classical Kac polynomials fn(x)=∑i=0nξ ixi where ξi are independent random variables with mean 0, variance 1, and uniformly bounded (2+ε0)-moments. We establish polynomial tail bounds, which are optimal, for the bulk of roots. For the whole real line, we establish sub-optimal tail bounds.
Authors
- Van Hao Can (ORCID: https://orcid.org/0000-0003-0070-7375)
- Oanh Kieu Nguyen (ORCID: https://orcid.org/0000-0002-4614-0215)
Institutions
- Brown University (US)
- Institute of Mathematics (VN)
- Vietnam Academy of Science and Technology (VN)
Publication Details
- Journal
- Electronic Journal of Probability
- Published
- 2025-01-01
- DOI
- https://doi.org/10.1214/25-ejp1328
- Citations
- 1
- Primary Topic
- Geometry and complex manifolds
- Type
- article
- Field-Weighted Citation Impact
- 4.09
Funders
- National Science Foundation
- National Foundation for Science and Technology Development