2022/08/17 更新

写真a

トゥリン カーン デュイ
トゥリン カーン デュイ
所属
理工学術院 国際理工学センター(理工学術院)
職名
准教授(任期付)

学内研究所等

  • 2020年
    -
    2022年

    理工学術院総合研究所   兼任研究員

経歴

  • 2019年04月
    -
    継続中

    Waseda University   Global Center for Science and Engineering   Associate Professor (without tenure)

  • 2017年12月
    -
    2019年03月

    Research Alliance Center for Mathematical Sciences, Tohoku University, Japan   Associate Professor

  • 2013年10月
    -
    2017年11月

    Institute of Mathematics for Industry, Kyushu University, Japan   Assistant Professor

  • 2012年07月
    -
    2013年09月

    Department of Mathematics, Graduate School of Science, Osaka University, Japan   Research Fellow of the Japan Society for the Promotion of Science

 

研究分野

  • 基礎解析学   Probability theory and applied probability

論文

  • Beta Laguerre processes in a high temperature regime

    Hoang Dung Trinh, Khanh Duy Trinh

    Stochastic Processes and their Applications   136   192 - 205  2021年06月

    DOI

  • Beta Laguerre ensembles in global regime

    Hoang Dung Trinh, Khanh Duy Trinh

    Osaka J. Math.   58 ( 2 ) 435 - 450  2021年04月  [査読有り]

  • Poisson Statistics for Beta Ensembles on the Real Line at High Temperature

    Fumihiko Nakano, Khanh Duy Trinh

    Journal of Statistical Physics   179 ( 2 ) 632 - 649  2020年04月

    DOI

  • On central limit theorems in stochastic geometry for add-one cost stabilizing functionals

    Khanh Duy Trinh

    Electronic Communications in Probability   24 ( none )  2019年12月

    DOI

  • Global Spectrum Fluctuations for Gaussian Beta Ensembles: A Martingale Approach

    Khanh Duy Trinh

    Journal of Theoretical Probability   32 ( 3 ) 1420 - 1437  2019年09月

    DOI

  • Strong Law of Large Numbers for Betti Numbers in the Thermodynamic Regime

    Akshay Goel, Khanh Duy Trinh, Kenkichi Tsunoda

    JOURNAL OF STATISTICAL PHYSICS   174 ( 4 ) 865 - 892  2019年02月  [査読有り]

     概要を見る

    We establish the strong law of large numbers for Betti numbers of random ech complexes built on RN-valued binomial point processes and related Poisson point processes in the thermodynamic regime. Here we consider both the case where the underlying distribution of the point processes is absolutely continuous with respect to the Lebesgue measure on RN and the case where it is supported on a C1 compact manifold of dimension strictly less than N. The strong law is proved under very mild assumption which only requires that the common probability density function belongs to Lp spaces, for all 1p<.

    DOI

  • Gaussian Beta Ensembles at High Temperature: Eigenvalue Fluctuations and Bulk Statistics

    Fumihiko Nakano, Khanh Duy Trinh

    Journal of Statistical Physics   173 ( 2 ) 295 - 321  2018年10月  [査読有り]

    DOI

  • On spectral measures of random Jacobi matrices

    Trinh Khanh Duy

    Osaka J. Math.   55 ( 4 ) 595 - 617  2018年10月  [査読有り]

  • Limit theorems for persistence diagrams

    Yasuaki Hiraoka, Tomoyuki Shirai, Khanh Duy Trinh

    Ann. Appl. Probab.   28 ( 5 ) 2740 - 2780  2018年10月  [査読有り]

    DOI

  • A remark on the convergence of Betti numbers in the thermodynamic regime

    Trinh Khanh Duy

    Pac. J. Math. Ind.   9 ( 4 ) 1 - 7  2017年03月  [査読有り]

    DOI

  • Distributions of the determinants of Gaussian beta ensembles

    Trinh Khanh Duy

    RIMS Kôkyûroku   2023   77 - 85  2017年

  • CENTRAL LIMIT THEOREM FOR MOMENTS OF SPECTRAL MEASURES OF WIGNER MATRICES

    Trinh Khanh Duy

    OSAKA JOURNAL OF MATHEMATICS   53 ( 1 ) 141 - 160  2016年01月  [査読有り]

     概要を見る

    Spectral measures of Wigner matrices are investigated. The Wigner semicircle law for spectral measures is proved. Regard this as the law of large number, the central limit theorem moments of spectral measures is also derived. The proof is based on moment method and combinatorial method.

    DOI

  • The mean spectral measures of random Jacobi matrices related to Gaussian beta ensembles

    Trinh Khanh Duy, Tomoyuki Shirai

    ELECTRONIC COMMUNICATIONS IN PROBABILITY   20 ( 68 ) 1 - 13  2015年09月  [査読有り]

     概要を見る

    An explicit formula for the mean spectral measure of a random Jacobi matrix is derived. The matrix can be regarded as the limit of Gaussian beta ensemble (G beta E) matrices as the matrix size N tends to infinity with the constraint that N beta is a constant.

    DOI

  • An Introduction to Ergodic Theory

    Khanh Duy Trinh

    A Mathematical Approach to Research Problems of Science and Technology     297  2014年  [査読有り]

    DOI

  • On the distribution of $k$-th power free integers, II

    Khanh Duy Trinh, Takanobu Satoshi

    Osaka J. Math.   50 ( 3 ) 687 - 713  2013年07月  [査読有り]

    DOI

  • On convergence of Fourier series of Besicovitch almost periodic functions

    Trinh Khanh Duy

    LITHUANIAN MATHEMATICAL JOURNAL   53 ( 3 ) 264 - 279  2013年07月  [査読有り]

     概要を見る

    The paper deals with convergence of the Fourier series of q-Besicovitch almost periodic functions of the form f(t) similar to Sigma(infinity)(m=1)a(m)e(-i lambda mt)
    where {lambda m} is a Dirichlet sequence, that is, a strictly increasing sequence of nonnegative numbers tending to infinity. In particular, we show that, for 1 &lt; q &lt; a, the Fourier series of f(t) converges in norm to the function f(t) itself with usual order, which is analogous to the convergence in norm of the Fourier series of a function on [0, 2 pi]. A version of the Carleson-Hunt theorem is also investigated.

    DOI

  • Probabilistic aspects of Besicovitch almost periodic functions

    Trinh Khanh Duy

    PhD Thesis. Osaka University    2012年06月

  • Remarks on value distributions of general Dirichlet series

    Duy Trinh Khanh

    Functions in number theory and their probabilistic aspects. RIMS Kôkyûroku Bessatsu   B34   49 - 68  2012年  [査読有り]

  • CARLESON'S THEOREM FOR GENERAL DIRICHLET SERIES

    Trinh Khanh Duy

    ANALYTIC AND PROBABILISTIC METHODS IN NUMBER THEORY     119 - 129  2012年  [査読有り]

     概要を見る

    This paper deals with a general Dirichlet series of the form
    Sigma(infinity)(m=1) a(m)e(-lambda ms), s = sigma + it is an element of C,
    where a(m) is an element of C, and {lambda(m)} is a strictly increasing sequence of nonnegative numbers tending to infinity. Let A be a subgroup of Rd, the real line with discrete topology, generated by (lambda(m)). The dual group of A is a compact group (Lambda) over cap with the normalized Haar measure v. Let x(lambda) be a character on (Lambda) over cap defined by x(lambda)(x) = x(lambda)(lambda is an element of A, x is an element of (Lambda) over cap). Then {x(lambda m)} is an orthonormal system in L-2((Lambda) over cap, nu). Thus, for any square summable sequence (a(m)), that is,
    Sigma(infinity)(m=1) vertical bar a(m)vertical bar(2) &lt; infinity,
    the series
    Sigma(infinity)(m=1) a(m) chi lambda(m)
    converges in L-2((Lambda) over cap, nu). Our main result claims that this series actually converges almost everywhere (with respect to the Haar measure nu). This result is analogous to Carleson's theorem for Fourier series and has some interesting consequences.

  • On the distribution of $k$-th power free integers

    Khanh Duy Trinh

    Osaka J. Math.   48 ( 4 ) 1027 - 1045  2011年10月  [査読有り]

    DOI

  • LIMIT-PERIODIC ARITHMETICAL FUNCTIONS AND THE RING OF FINITE INTEGRAL ADELES

    Trinh Khanh Duy

    LITHUANIAN MATHEMATICAL JOURNAL   51 ( 4 ) 486 - 506  2011年10月  [査読有り]

     概要を見る

    In this paper, we show that the ring of finite integral adeles, together with its Borel field and its normalized Haar measure, is an appropriate probability space where limit-periodic arithmetical functions can be extended to random variables. The natural extensions of additive and multiplicative functions are studied. Besides, the convergence of Fourier expansions of limit-periodic functions is proved.

    DOI

  • On index-2 linear implicit difference equations

    Nguyen Huu Du, Le Cong Loi, Trinh Khanh Duy, Vu Tien Viet

    LINEAR ALGEBRA AND ITS APPLICATIONS   434 ( 2 ) 394 - 414  2011年01月  [査読有り]

     概要を見る

    This paper deals with an index-2 notion for linear implicit difference equations (LIDEs) and with the solvability of initial value problems (IVPs) for index-2 LIDEs. Besides, the cocycle property as well as the multiplicative ergodic theorem of Oseledets type are also proved. (C) 2010 Elsevier Inc. All rights reserved.

    DOI

  • Degenerate cocycle with index-1 and Lyapunov exponents

    Nguyen Huu Du, Trinh Khanh Duy, Vu Tien Viet

    STOCHASTICS AND DYNAMICS   7 ( 2 ) 229 - 245  2007年06月  [査読有り]

     概要を見る

    This paper deals with the solvability of initial-value problem and with Lyapunov exponents for linear implicit random difference equations, i.e. the difference equations where the leading term cannot be solved. An index-1 concept for linear implicit random difference equations is introduced and a formula of solutions is given. Paper is also concerned with a version of the multiplicative theorem of Oseledets type.

    DOI DOI2

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