Concentration of the number of real roots of random polynomials

Ander Aguirre; Hoi H. Nguyen; Jingheng Wang

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arXiv · 2402.08773

Concentration of the number of real roots of random polynomials

Ander Aguirre·Hoi H. Nguyen·Jingheng Wang

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Abstract

Many statistics of roots of random polynomials have been studied in the literature, but not much is known on the concentration aspect. In this note we present a systematic study of this question, aiming towards nearly optimal bounds to some extent. Our method is elementary and works well for many models of random polynomials, with gaussian or non-gaussian coefficients.

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Ander Aguirre, Hoi H. Nguyen, Jingheng Wang. 2024-02-13. Concentration of the number of real roots of random polynomials. https://arxiv.org/abs/2402.08773

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