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- W2942973904 abstract "This paper seeks to further explore the distribution of the real roots of random polynomials with non-centered coefficients. We focus on polynomials where the typical values of their coefficients have power growth (or mild decay) and count the average number of real zeros inside local and global intervals. Almost all previous results require coefficients with zero mean, and it is highly non-trivial to extend these results to the general case. Our approach is based on a novel comparison principle, allowing us to reduce the general situation to the mean-zero setting. As applications, we obtain new results for the Kac polynomials, hyperbolic random polynomials, their derivatives, and generalizations of these polynomials. The proof features new logarithmic integrability estimates for random polynomials (both local and global) and fairly sharp estimates for the local number of real zeros." @default.
- W2942973904 created "2019-05-09" @default.
- W2942973904 creator A5005483725 @default.
- W2942973904 date "2019-05-06" @default.
- W2942973904 modified "2023-09-27" @default.
- W2942973904 title "Real roots of random polynomials with coefficients of polynomial growth and non-zero means: a comparison principle and applications" @default.
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