Work

Concentration inequalities for the number of real zeros of Kac polynomials

Year: 2025

Type: article

Abstract: 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.

Source: Electronic Journal of Probability

DOI: 10.1214/25-ejp1328

Authors: Van Hao Can, Oanh Nguyen

Institutions: Institute of Mathematics, Vietnam Academy of Science and Technology, Brown University

Language: English

Topic: Random Matrices and Applications

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $675

Funders: National Science Foundation, National Foundation for Science and Technology Development, Vietnam Academy of Science and Technology