Kawabi, Hiroshi

写真a

Affiliation

Faculty of Economics （Hiyoshi）

Position

Professor
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Papers 【 Display / hide 】

  • Stochastic quantization associated with the exp (Φ) <inf>2</inf> -quantum field model driven by space-time white noise on the torus in the full L<sup>1</sup> -regime

    Hoshino M., Kawabi H., Kusuoka S.

    Probability Theory and Related Fields （Probability Theory and Related Fields)  185 （ 1-2 ） 391 - 447 2023.02

    ISSN  01788051

    　View Summary

    The present paper is a continuation of our previous work (Hoshino et al., J Evol Equ 21:339–375, 2021) on the stochastic quantization of the exp (Φ) 2-quantum field model on the two-dimensional torus. Making use of key properties of Gaussian multiplicative chaos and refining the method for singular SPDEs introduced in the previous work, we construct a unique time-global solution to the corresponding parabolic stochastic quantization equation in the full “L1-regime” |α|<8π of the charge parameter α. We also identify the solution with an infinite-dimensional diffusion process constructed by the Dirichlet form approach.

  • Central Limit Theorems for Non-Symmetric Random Walks on Nilpotent Covering Graphs: Part II

    Ishiwata S., Kawabi H., Namba R.

    Potential Analysis （Potential Analysis)  55 （ 1 ） 127 - 166 2021.06

    ISSN  09262601

    　View Summary

    In the present paper, as a continuation of our preceding paper (Ishiwata et al. 2018), we study another kind of central limit theorems (CLTs) for non-symmetric random walks on nilpotent covering graphs from a view point of discrete geometric analysis developed by Kotani and Sunada. We introduce a one-parameter family of random walks which interpolates between the original non-symmetric random walk and the symmetrized one. We first prove a semigroup CLT for the family of random walks by realizing the nilpotent covering graph into a nilpotent Lie group via discrete harmonic maps. The limiting diffusion semigroup is generated by the homogenized sub-Laplacian with a constant drift of the asymptotic direction on the nilpotent Lie group, which is equipped with the Albanese metric associated with the symmetrized random walk. We next prove a functional CLT (i.e., Donsker-type invariance principle) in a Hölder space over the nilpotent Lie group by combining the semigroup CLT, standard martingale techniques, and a novel pathwise argument inspired by rough path theory. Applying the corrector method, we finally extend these CLTs to the case where the realizations are not necessarily harmonic.

  • Stochastic quantization associated with the exp (Φ) <inf>2</inf> -quantum field model driven by space-time white noise on the torus

    Hoshino M., Kawabi H., Kusuoka S.

    Journal of Evolution Equations （Journal of Evolution Equations)  21 （ 1 ） 339 - 375 2021.03

    ISSN  14243199

    　View Summary

    We consider a quantum field model with exponential interactions on the two-dimensional torus, which is called the exp (Φ) 2-quantum field model or Høegh-Krohn’s model. In the present paper, we study the stochastic quantization of this model by singular stochastic partial differential equations, which is recently developed. By the method, we construct a unique time-global solution and the invariant probability measure of the corresponding stochastic quantization equation and identify it with an infinite-dimensional diffusion process, which has been constructed by the Dirichlet form approach.

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

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

  • 幾何解析の視点を融合した無限次元空間上の確率解析の新展開

    2023.04
    -
    2026.03

    基盤研究(C), Principal investigator

  • Stochastic Analysis on Infinite Dimensional Spaces from a Geometric View

    2020.04
    -
    2023.03

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

  • Research on differential operators on infinite dimensional spaces via stochastic analysis

    2017.04
    -
    2020.03

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

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Courses Taught 【 Display / hide 】

  • MATHEMATICS FOR ECONOMICS

    2023

  • INTRODUCTION TO PROBABILITY THEORY 2

    2023

  • INTRODUCTION TO PROBABILITY THEORY 1

    2023

  • INTRODUCTION TO CALCULUS

    2023

  • CALCULUS

    2023

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