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math.PR2026
Real roots of non-centered random polynomials
Yen Q. Do, Nhan D. V. Nguyen, Sean O'Rourke
We study the fluctuations of the number of real roots of random polynomials with independent, nonzero-mean coefficients. Such non-centered ensembles arise naturally in signal-plus-…
math.PR2025
Real roots of random polynomials: asymptotics of the variance
Yen Q. Do, Nhan D. V. Nguyen
We compute the precise leading asymptotics of the variance of the number of real roots for a large class of random polynomials, where the random coefficients have polynomial growth…