19 citations · 73 across the 23 of their papers we have counts for
12 papers · 1 filter
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-…
A strong law of large numbers for real roots of random polynomials
Yen Q. Do
We consider random polynomials whose coefficients are independent and identically distributed with zero mean, unit variance, and bounded …
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…
Real roots of random orthogonal polynomials with exponential weights
Yen Do, Doron Lubinsky, Hoi H. Nguyen +2
We consider random orthonormal polynomials where , . . . , are independent random variables with zero mean, unit variance…
Central Limit Theorem for the number of real roots of random orthogonal polynomials
Yen Do, Hoi H. Nguyen, Oanh Nguyen +1
In this note we study the number of real roots of a wide class of random orthogonal polynomials with gaussian coefficients. Using the method of Wiener Chaos we show that the fluctu…
Random orthonormal polynomials: local universality and expected number of real roots
Yen Do, Oanh Nguyen, Van Vu
We consider random orthonormal polynomials where , \dots, are independent random variables with zero mean, unit variance…
Random trigonometric polynomials: universality and non-universality of the variance for the number of real roots
Yen Do, Hoi H. Nguyen, Oanh Nguyen
In this paper, we study the number of real roots of random trigonometric polynomials with iid coefficients. When the coefficients have zero mean, unit variance and some finite high…
Real roots of random polynomials with coefficients of polynomial growth: a comparison principle and applications
Yen Q. Do
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 the…
Central limit theorems for the real zeros of Weyl polynomials
Yen Do, Van Vu
We establish the central limit theorem for the number of real roots of the Weyl polynomial , where are iid Gaussian rando…
Roots of random polynomials with coefficients having polynomial growth
Yen Do, Oanh Nguyen, Van Vu
In this paper, we prove optimal local universality for roots of random polynomials with arbitrary coeffcients of polynomial growth. As an application, we derive, for the first time…
Real roots of random polynomials: expectation and repulsion
Yen Do, Hoi Nguyen, Van Vu
Let be a Kac random polynomial where the coefficients are iid copies of a given random variable . Our main result is an optimal quantitati…
The spectrum of random kernel matrices: universality results for rough and varying kernels
Yen Do, Van Vu
We consider random matrices whose entries are f(<Xi,Xj>) or f(||Xi-Xj||^2) for iid vectors Xi in R^p with normalized distribution. Assuming that f is sufficiently smooth and the di…