Tanemura, Hideki

写真a

Affiliation

Faculty of Science and Technology, Department of Mathematics (Yagami)

Position

Professor

Career 【 Display / hide

  • 2018.04
    -
    Present

    Keio University, Faculty of Sience and Technology, Professor

  • 1989.09
    -
    1994.01

    Chiba University, Faculty of Science, Assistant

  • 1994.02
    -
    2005.11

    Chiba University, Faculty of Science, Associated Professor

  • 2005.12
    -
    2018.03

    Chiba University, Faculty of Science, Professor

Academic Background 【 Display / hide

  • 1978.04
    -
    1982.03

    Keio University, Faculty of Technology, Department of Mathematics

    University, Graduated

  • 1982.04
    -
    1984.03

    Keio University, 工学研究科, 数理工学

    Graduate School, Completed, Master's course

  • 1984.04
    -
    1989.03

    Keio University, 理工学研究科, 数理科学専攻

    Graduate School, Completed, Doctoral course

  • 1989.04
    -
    1989.08

    Keio University, 理工学研究科, 数理科学専攻

    Other, Other

Academic Degrees 【 Display / hide

  • Doctor of Science, Keio University, 1989.03

 

Papers 【 Display / hide

  • Infinite-dimensional stochastic differential equations and tail σ-fields II: the IFC condition

    Kawamoto Y., Osada H., Tanemura H.

    Journal of the Mathematical Society of Japan (Journal of the Mathematical Society of Japan)  74 ( 1 ) 79 - 128 2022

    ISSN  00255645

     View Summary

    In a previous report, the second and third authors gave general theorems for unique strong solutions of infinite-dimensional stochastic differential equations (ISDEs) describing the dynamics of infinitely many interacting Brownian particles. One of the critical assumptions is the “IFC” condition. The IFC condition requires that, for a given weak solution, the scheme consisting of the finite-dimensional stochastic differential equations (SDEs) related to the ISDEs exists. Furthermore, the IFC condition implies that each finite-dimensional SDE has unique strong solutions. Unlike other assumptions, the IFC condition is challenging to verify, and so the previous report only verified it for solutions given by quasi-regular Dirichlet forms. In the present paper, we provide a sufficient condition for the IFC requirement in more general situations. In particular, we prove the IFC condition without assuming the quasi-regularity or symmetry of the associated Dirichlet forms. As an application of the theoretical formulation, the results derived in this paper are used to prove the uniqueness of Dirichlet forms and the dynamical universality of random matrices.

  • Uniqueness of Dirichlet Forms Related to Infinite Systems of Interacting Brownian Motions

    Kawamoto Y., Osada H., Tanemura H.

    Potential Analysis (Potential Analysis)  55 ( 4 ) 639 - 676 2021.12

    ISSN  09262601

     View Summary

    The Dirichlet forms related to various infinite systems of interacting Brownian motions are studied. For a given random point field μ, there exist two natural infinite-volume Dirichlet forms (Eupr, Dupr) and (Elwr, Dlwr) on L2(S,μ) describing interacting Brownian motions each with unlabeled equilibrium state μ. The former is a decreasing limit of a scheme of such finite-volume Dirichlet forms, and the latter is an increasing limit of another scheme of such finite-volume Dirichlet forms. Furthermore, the latter is an extension of the former. We present a sufficient condition such that these two Dirichlet forms are the same. In the first main theorem (Theorem 3.1) the Markovian semi-group given by (Elwr, Dlwr) is associated with a natural infinite-dimensional stochastic differential equation (ISDE). In the second main theorem (Theorem 3.2), we prove that these Dirichlet forms coincide with each other by using the uniqueness of weak solutions of ISDE. We apply Theorem 3.1 to stochastic dynamics arising from random matrix theory such as the sine, Bessel, and Ginibre interacting Brownian motions and interacting Brownian motions with Ruelle’s class interaction potentials, and Theorem 3.2 to the sine2 interacting Brownian motion and interacting Brownian motions with Ruelle’s class interaction potentials of C03-class.

  • Infinite-dimensional stochastic differential equations and tail σ -fields

    Osada H., Tanemura H.

    Probability Theory and Related Fields (Probability Theory and Related Fields)  177 ( 3-4 ) 1137 - 1242 2020.08

    ISSN  01788051

     View Summary

    We present general theorems solving the long-standing problem of the existence and pathwise uniqueness of strong solutions of infinite-dimensional stochastic differential equations (ISDEs) called interacting Brownian motions. These ISDEs describe the dynamics of infinitely-many Brownian particles moving in Rd with free potential Φ and mutual interaction potential Ψ. We apply the theorems to essentially all interaction potentials of Ruelle’s class such as the Lennard-Jones 6-12 potential and Riesz potentials, and to logarithmic potentials appearing in random matrix theory. We solve ISDEs of the Ginibre interacting Brownian motion and the sineβ interacting Brownian motion with β= 1 , 2 , 4. We also use the theorems in separate papers for the Airy and Bessel interacting Brownian motions. One of the critical points for proving the general theorems is to establish a new formulation of solutions of ISDEs in terms of tail σ-fields of labeled path spaces consisting of trajectories of infinitely-many particles. These formulations are equivalent to the original notions of solutions of ISDEs, and more feasible to treat in infinite dimensions.

Papers, etc., Registered in KOARA 【 Display / hide

Research Projects of Competitive Funds, etc. 【 Display / hide

  • Stochastic analysis for phase transition in particle systems with an infinite number of particles

    2019.04
    -
    2024.03

    MEXT,JSPS, Grant-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (B), Principal investigator

 

Courses Taught 【 Display / hide

  • TOPICS IN PROBABILITY THEORY A

    2022

  • TOPICS IN LIFE INSURANCE MATHEMATICS

    2022

  • PROBABILITY THEORY 1 AND ITS EXERCISE

    2022

  • MATHEMATICS 1B

    2022

  • MATHEMATICS 1A

    2022

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