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Yen Do

University of Virginia · Mathematics

Active 2009–2024

h-index10
Citations303
Papers4113 last 5y
Funding$318k

Academic metrics are sourced from OpenAlex and public funding records; values may differ from Google Scholar.

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About

Yen Do is an Associate Professor in the Department of Mathematics at the University of Virginia. His research focuses on Harmonic Analysis, Random Polynomials, Analysis, Probability, and related areas. He is involved in teaching and mentoring students, and maintains a personal webpage with additional information about his work and interests.

Research topics

  • Mathematics
  • Pure mathematics
  • Combinatorics
  • Mathematical analysis
  • Discrete mathematics

Selected publications

  • Central Limit Theorems for the Real Zeros of Weyl Polynomials

    American Journal of Mathematics · 2020-01-01 · 13 citations

    article1st authorCorresponding

    We establish the central limit theorem for the number of real roots of the Weyl polynomial $P_n(x)=\xi_0+\xi_1 x+\cdots+{1\over\sqrt{n!}}\xi_n x^n$, where $\xi_i$ are iid Gaussian random variables. The main ingredients in the proof are new estimates for the correlation functions of the real roots of $P_n$ and a comparison argument exploiting local laws and repulsion properties of these real roots.

    PublisherDOI

  • Random trigonometric polynomials: Universality and non-universality of the variance for the number of real roots

    Annales de l Institut Henri Poincaré Probabilités et Statistiques · 2022-07-15 · 12 citations

    article1st authorCorresponding

    Dans cet article, nous étudions le nombre de zéros réels de polynômes trigonométriques avec coefficients i.i.d. Quand les coefficients sont centrés, réduits, et possèdent des moments finis d’ordre suffisamment élevé, nous montrons que la variance du nombre de zéros est asymptotiquement linéaire en son espérance ; de plus, la constante multiplicative dans cette relation linéaire dépend seulement du kurtosis de la loi commune des coefficients du polynôme. Ce résultat contraste fortement avec les c…

    PublisherDOI

  • Variation-norm and fluctuation estimates for ergodic bilinear averages

    Indiana University Mathematics Journal · 2017-01-01 · 12 citations

    article1st authorCorresponding

    Abstract. 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 follows that, with probability one, the number of fluctuations along this sequence may grow at most polynomially with respect to (the growth of) the underlying scale. These results strengthen previous works of Lacey and Bourgain where almost surely convergence of the sequence was proved (which is equivalent to th…

    PublisherDOI

  • Variational estimates for the bilinear iterated Fourier integral

    Journal of Functional Analysis · 2016-09-22 · 9 citations

    article1st authorCorresponding
    PublisherDOI

  • Roots of random polynomials with coefficients having polynomial growth

    arXiv (Cornell University) · 2015-07-17 · 7 citations

    preprintOpen access1st authorCorresponding

    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, sharp estimates for the number of real roots of these polynomials, even when the coeffcients are not explicit. Our results also hold for series; in particular, we prove local universality for random hyperbolic series.

    PublisherOA PDFDOI

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Education

  • PhD, Mathematics

    University of California at Los Angeles

    2010

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