19 citations · 73 across the 23 of their papers we have counts for
24 papers
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…
Generalized Carleson Embeddings into Weighted Outer Measure Spaces
Yen Do, Mark Lewers
We prove generalized Carleson embeddings for the continuous wave packet transform from into an outer space for and weight .…
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…
Oscillations and integrability of the vorticity in the 3D NS flows
Y. Do, A. Farhat, Z. Grujic +1
In the studies of the Navier-Stokes (NS) regularity problem, it has become increasingly clear that a more realistic path to improved a priori bounds is to try to break away from th…
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…
Positive sparse domination of variational Carleson operators
Francesco Di Plinio, Yen Q. Do, Gennady N. Uraltsev
Due to its nonlocal nature, the -variation norm Carleson operator does not yield to the sparse domination techniques of Lerner, Di Plinio and Lerner, Lacey. We overcome th…
Variational estimates for the bilinear iterated Fourier integral
Yen Do, Camil Muscalu, Christoph Thiele
We prove pointwise variational Lp bounds for a bilinear Fourier integral operator in a large but not necessarily sharp range of exponents. This result is a joint strengthening of t…
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…
Variation-norm and fluctuation estimates for ergodic bilinear averages
Yen Do, Richard Oberlin, Eyvindur A. Palsson
For any dynamical system, we show that higher variation-norms for the sequence of ergodic bilinear averages of two functions satisfy a large range of bilinear Lp estimates. It foll…
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…
Lp theory for outer measures and two themes of Lennart Carleson united
Yen Do, Christoph Thiele
We develop a theory of Lp spaces based on outer measures rather than measures. This theory includes the classical Lp theory on measure spaces as special case. It also covers parts…
An operator van der Corput estimate arising from oscillatory Riemann-Hilbert problems
Yen Do, Philip T. Gressman
We study an operator analogue of the classical problem of finding the rate of decay of an oscillatory integral on the real line. This particular problem arose in the analysis of os…
Weighted bounds for variational Fourier series
Yen Do, Michael Lacey
For 1<p<infty and for weight w in A_p, we show that the r-variation of the Fourier sums of any function in L^p(w) is finite a.e. for r larger than a finite constant depending on w…
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…
Weighted bounds for variational Walsh-Fourier series
Michael T. Lacey, Yen Do
For 1<p<infty, and weight w in A_p, and function f in L^p(w), we show that the r-variation of the Walsh-Fourier sums are finite, for r sufficiently large as function of w. (That r…
On the Convergence of Lacunary Walsh-Fourier Series
Yen Do, Michael T. Lacey
We study the Walsh-Fourier series of S_{n_j}f, along a lacunary subsequence of integers {n_j}. Under a suitable integrability condition, we show that the sequence converges to f a.…
Variational estimates for paraproducts
Yen Do, Camil Muscalu, Christoph Thiele
We generalize a family of variation norm estimates of Lepingle with endpoint estimates of Bourgain and Pisier-Xu to a family of variational estimates for paraproducts, both in the…
A nonlinear stationary phase method for oscillatory Riemann-Hilbert problems
Yen Do
We study the asymptotic behavior of oscillatory Riemann-Hilbert problems arising in the AKNS hierarchy of integrable nonlinear PDE's. Our method is based on the Deift-Zhou nonlinea…