KEIO RESEARCHERS INFORMATION SYSTEM

Papers 【 Display / hide 】

Papers 【 Display / hide 】

• A graph discretized approximation of semigroups for diffusion with drift and killing on a complete Riemannian manifold

  Ishiwata S., Kawabi H.

  Mathematische Annalen 390 ( 2 ) 2459 - 2495 2024.10

  ISSN  00255831

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  In the present paper, we prove that the C<inf>0</inf>-semigroup generated by a Schrödinger operator with drift on a complete Riemannian manifold is approximated by the discrete semigroups associated with a family of discrete time random walks with killing in a flow on a sequence of proximity graphs, which are constructed by partitions of the manifold. Furthermore, when the manifold is compact, we also obtain a quantitative error estimate of the convergence. Finally, we give examples of the partition of the manifold and the drift term on two typical manifolds: Euclidean spaces and model manifolds.

  • Access to Document (DOI)

• 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 L¹ -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

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  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.

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• Strong uniqueness for Dirichlet operators related to stochastic quantization under exponential/trigonometric interactions on the two-dimensional torus

  Albeverio S., Kawabi H., Mihalache S.R., Röckner M.

  Annali Della Scuola Normale Superiore Di Pisa Classe Di Scienze 24 ( 1 ) 33 - 69 2023

  ISSN  0391173X

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  We consider space-time quantum fields with exponential/trigonometric interactions. In the context of Euclidean quantum field theory, the former and the latter are called the Høegh-Krohn model and the Sine-Gordon model, respectively. The main objective of the present paper is to construct infinite dimensional diffusion processes which solve modified stochastic quantization equations for these quantum fields on the two-dimensional torus by the Dirichlet form approach and to prove strong uniqueness of the corresponding Dirichlet operators.

  • Access to Document (DOI)

• 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

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  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.

  • Access to Document (DOI)

• 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.

  • Access to Document (DOI)

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

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

• Stochastic analysis on infinite dimensional spaces from a geometric view

  Kawabi, Hiroshi

  科学研究費補助金研究成果報告書 2023

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

  Kawabi, Hiroshi

  科学研究費補助金研究成果報告書 2021

• On a precise long time asymptotics of non-symmetric random walks on nilpotent covering graphs and its application

  Kawabi, Hiroshi

  学事振興資金研究成果実績報告書 (慶應義塾大学)  2018

• A remark on default risk models

  Kawabi, Hiroshi

  Keio journal of economics (慶應義塾経済学会)  92 ( 3 ) 507(51) - 521(65) 1999.10

  ISSN  00266760

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

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

Courses Taught 【 Display / hide 】

Courses Taught 【 Display / hide 】

• CALCULUS

  2026

• MATHEMATICS FOR ECONOMICS

  2026

• MATHEMATICS FOR ECONOMICS 1

  2026

• MATHEMATICS FOR ECONOMICS 2

  2026

• INTRODUCTION TO CALCULUS

  2026

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