Updated on 2022/07/02

写真a

 
TRINH, Khanh Duy
 
Affiliation
Faculty of Science and Engineering, Global Center for Science and Engineering
Job title
Associate Professor(without tenure)

Research Institute

  • 2020
    -
    2022

    理工学術院総合研究所   兼任研究員

Research Experience

  • 2019.04
    -
    Now

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

  • 2017.12
    -
    2019.03

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

  • 2013.10
    -
    2017.11

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

  • 2012.07
    -
    2013.09

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

 

Research Areas

  • Basic analysis   Probability theory and applied probability

Papers

  • Beta Laguerre processes in a high temperature regime

    Hoang Dung Trinh, Khanh Duy Trinh

    Stochastic Processes and their Applications   136   192 - 205  2021.06

    DOI

  • Beta Laguerre ensembles in global regime

    Hoang Dung Trinh, Khanh Duy Trinh

    Osaka J. Math.   58 ( 2 ) 435 - 450  2021.04  [Refereed]

  • 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  2020.04

    DOI

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

    Khanh Duy Trinh

    Electronic Communications in Probability   24 ( none )  2019.12

    DOI

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

    Khanh Duy Trinh

    Journal of Theoretical Probability   32 ( 3 ) 1420 - 1437  2019.09

    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  2019.02  [Refereed]

     View Summary

    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  2018.10  [Refereed]

    DOI

  • On spectral measures of random Jacobi matrices

    Khanh Duy Trinh

    Osaka J. Math.   55 ( 4 ) 595 - 617  2018.10  [Refereed]

  • Limit theorems for persistence diagrams

    Yasuaki Hiraoka, Tomoyuki Shirai, Khanh Duy Trinh

    Ann. Appl. Probab.   28 ( 5 ) 2740 - 2780  2018.10  [Refereed]

    DOI

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

    Khanh Duy Trinh

    Pac. J. Math. Ind.   9 ( 4 ) 1 - 7  2017.03  [Refereed]

    DOI

  • Distributions of the determinants of Gaussian beta ensembles

    Khanh Duy Trinh

    RIMS Kôkyûroku   2023   77 - 85  2017

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

    Trinh Khanh Duy

    OSAKA JOURNAL OF MATHEMATICS   53 ( 1 ) 141 - 160  2016.01  [Refereed]

     View Summary

    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  2015.09  [Refereed]

     View Summary

    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  [Refereed]

    DOI

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

    Khanh Duy Trinh, Takanobu Satoshi

    Osaka J. Math.   50 ( 3 ) 687 - 713  2013.07  [Refereed]

    DOI

  • On convergence of Fourier series of Besicovitch almost periodic functions

    Trinh Khanh Duy

    LITHUANIAN MATHEMATICAL JOURNAL   53 ( 3 ) 264 - 279  2013.07  [Refereed]

     View Summary

    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

    Khanh Duy Trinh

    PhD Thesis. Osaka University    2012.06

  • 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  [Refereed]

  • CARLESON'S THEOREM FOR GENERAL DIRICHLET SERIES

    Trinh Khanh Duy

    ANALYTIC AND PROBABILISTIC METHODS IN NUMBER THEORY     119 - 129  2012  [Refereed]

     View Summary

    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  2011.10  [Refereed]

    DOI

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

    Trinh Khanh Duy

    LITHUANIAN MATHEMATICAL JOURNAL   51 ( 4 ) 486 - 506  2011.10  [Refereed]

     View Summary

    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  2011.01  [Refereed]

     View Summary

    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  2007.06  [Refereed]

     View Summary

    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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Misc

  • On persistent homology of random Cech complexes (Stochastic Analysis on Large Scale Interacting Systems)

    Trinh Khanh Duy

      ( 79 ) 215 - 228  2020.04

     View Summary

    The paper studies the relation between critical simplices and persistence diagrams of the Cech filtration. We show that adding a critical k-simplex into the filtration corresponds either to a point in the kth persistence diagram or a point in the (k - 1)st persistence diagram. Consequently, the number of points in persistence diagrams can be expressed in terms of the number of critical simplices. As an application, we establish some convergence results related to persistence diagrams of the Cech filtrations built over binomial point processes.

    CiNii

 

Syllabus

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