Rchr
J-GLOBAL ID:200901031303577492
Update date: Feb. 12, 2024
Kumagai Takashi
クマガイ タカシ | Kumagai Takashi
Affiliation and department:
Job title:
Professor,Professor
Homepage URL (1):
https://t-kumagai.w.waseda.jp
Research field (2):
Applied mathematics and statistics
, Basic mathematics
Research keywords (2):
確率論
, Probability Theory
Research theme for competitive and other funds (68):
- 2023 - 2027 Theory for convergence of discrete surfaces with conformal structures
- 2022 - 2027 Stochastic Processes and Stochastic Analysis on Disordered Media
- 2023 - 2026 Macroscopic properties of discrete stochastic models and analysis of their scaling limits
- 2021 - 2024 Study of Analysis and Geometry of complex spaces
- 2017 - 2022 Anomalous diffusions on disordered media
- 2016 - 2021 Stochastic Analysis on Infinite Particle Systems
- 2017 - 2020 Dynamics on Random Media
- 2017 - 2020 Relation between structure of spaces and analysis
- 2015 - 2019 Research on Markov processes via stochastic analysis
- 2015 - 2019 Development of probability theory and geometry based on local structures induced by Dirichlet forms
- 2014 - 2019 Stochastic analysis on large scale interacting systems and its development
- 2014 - 2018 Potential theory for non-local operators
- 2016 - 2017 無限粒子系とランダム行列の確率解析
- 2014 - 2017 Relation between algebra, geometry and analysis on fractals
- 2014 - 2017 Stochastic analytic study on Kardar-Parisi-Zhang equation
- 2013 - 2017 Stochastic processes on disordered media -- discrete models and their scaling limits
- 2013 - 2017 Potential theory on space complexity and ideal boundary
- 2012 - 2017 Discrete Geometric Analysis for Quantum Spin System
- 2014 - 2016 Towerd analysis on metric-measure spaces-- Cheeger theory and fractals
- 2012 - 2016 Stochastic geometry and dynamics of infinite particle systems interacting with two-dimensional Coulomb potential
- 2010 - 2015 Stochastic analysis on large scale interacting systems and its applications
- 2012 - 2014 Towards de Giorgi-Nash-Moser theory on non-linear non-local partial differential equations.
- 2011 - 2014 Interaction between areas of Mathematics related to internal structures of fractals
- 2009 - 2014 Infinite dimensional stochastic analysis and geometry
- 2010 - 2013 Markov chains on disordered media and their scaling limits
- 2009 - 2012 Geometric properties on the threshold of the Sobolev type inequalities and generalization to metric spaces
- 2008 - 2012 Research on potential problems from various aspects
- 2008 - 2011 Study of Geometry of a discrete space through randomness
- 2009 - 2010 低次元臨界確率パーコレーション上のダイナミックスとそのスケール極限
- 2008 - 2010 Aspects of Mathematics on Fractals
- 2007 - 2010 Theory of stochastic analysis and its applications
- 2006 - 2009 Geometry and Invariants of 3-manifolds
- 2006 - 2009 Stochastic analysis on large scale interacting systems
- 2006 - 2008 Developments of the theory of stochastic processes and real analysis on disordered media
- 2006 - 2008 Geometric property of the Gaussian estimate of the gradient of the heat kernel
- 2005 - 2008 Comprehensive and integrated research of problems motivated by statistical mechanics with stochastic analysis
- 2005 - 2008 Stochastic analysis in infinite dimensional spaces
- 2006 - 2007 臨界確率における確率モデル上の熱伝導の研究
- 2005 - 2007 Aspects of Mathematics on Fractals
- 2005 - 2006 測度論的リーマン構造と対応する熱核の漸近挙動
- 2004 - 2005 ハルナック不等式の安定性とその確率モデルへの応用
- 2004 - 2005 Stability of Harnack inequalities and the applications to stochastic models
- 2002 - 2005 A study of stochastic analysis - synthesizing and integrating
- 2002 - 2004 Integrated research of Probability Theory
- 2002 - 2004 Mathematical Fundation of Fractals
- 2002 - 2003 INteraction between probability and analysis on disordered media
- 2002 - 2003 多変数複素力学系とフラクタル上のラプラシアンのスペクトル分布の接点
- 2001 - 2003 Aspects of large deviation principles
- 2001 - 2003 複雑集合の内と外のポテンシャル解析
- 2001 - 2001 確率解析に関する国際研究集会のための企画調査
- 2000 - 2001 複雑度の高い空間における確率解析の研究
- 1999 - 2001 Analysis of sample paths for stochastic processes
- 1999 - 2000 Research on vibrations and diffusions on fractals
- 1998 - 2000 Developments of Analysis on Fractals
- 1998 - 1999 スピングラスの確立論的研究
- 1997 - 1999 Probability Theory and Its Interface
- 1996 - 1999 Studies of Turbulence as a Nonlinear Science
- 1996 - 1997 Research of stochastic processes on fractals.
- 1996 - 1996 量子確率過程の超関数論的研究
- 1995 - 1996 General research of Probability theory
- 1994 - 1996 Stochastic processes with applications to statistical mechanics
- 1995 - 1995 ホワイトノイズによる量子確率解析とその応用
- 1993 - 1993 フラクタル上の拡散過程の研究
- 1992 - 1992 双曲型偏微分方程式の解の構造の研究
- 無限粒子系の解析
- フラクタル上の解析
- Analysis on infinite particle systems
- Analysis on fractals
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Papers (111):
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Sebastian Andres, David Croydon, Takashi Kumagai. Heat Kernel Fluctuations for Stochastic Processes on Fractals and Random Media. Applied and Numerical Harmonic Analysis. 2023. 265-281
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Zhen Qing Chen, Panki Kim, Takashi Kumagai, Jian Wang. HEAT KERNELS FOR REFLECTED DIFFUSIONS WITH JUMPS ON INNER UNIFORM DOMAINS. Transactions of the American Mathematical Society. 2022. 375. 10. 6797-6841
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Zhen-Qing Chen, Takashi Kumagai, Jian Wang. Heat kernel estimates for general symmetric pure jump Dirichlet forms. ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE. 2022. 1091-1140
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Moritz Kassmann, Kyung Youn Kim, Takashi Kumagai. Heat kernel bounds for nonlocal operators with singular kernels. Journal des Mathematiques Pures et Appliquees. 2022. 164. 1-26
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V.-H. Can, D.A. Croydon, T. Kumagai. Spectral dimension of simple random walk on a long-range percolation cluster. Electron. J. Probab. 2022. 27. 56. 1-37
more...
MISC (11):
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熊谷 隆. フィールズ賞で語る現代数学 21 ー確率論. 数理科学. 2018. 61-67
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熊谷 隆. ランダム媒質とフラクタル. 数学セミナー. 2017. 56. 3. 26-31
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熊谷 隆. 数理科学への確率論によるアプローチ. 数理科学. 2016. 5-6
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Zhen-Qing Chen, Panki Kim, Takashi Kumagai. GLOBAL HEAT KERNEL ESTIMATES FOR SYMMETRIC JUMP PROCESSES (vol 363, pg 5021, 2011). TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. 2015. 367. 10. 7515-7515
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Kumagai Takashi. Random conductance models on $\mathbb{Z}^d$ (Stochastic Processes and Statistical Phenomena behind PDEs). RIMS Kokyuroku. 2013. 1823. 97-106
more...
Books (11):
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Limit theorems for some long range random walks on torsion free nilpotent groups
Springer 2023 ISBN:9783031433313
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Stability of heat kernel estimates for symmetric non-local Dirichlet forms
American Mathematical Society 2021 ISBN:9781470448639
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Random Walks on Disordered Media and their Scaling Limits.
Springer 2014
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Probabilistic approach to geometry
Mathematical Society of Japan 2010 ISBN:9784931469587
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Homogenization on finitely ramified fractals
Advanced Studies in Pure Math., 41, Stochastic Analysis and Related Topics in Kyoto (H. Kunita et al. (eds.)), MSJ,189-207 2004
more...
Lectures and oral presentations (96):
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Heat kernel fluctuations and quantitative homogenizations for the one dimensional Bouchaud trap model
(Random Interacting Systems, Scaling Limits, and Universality at IMS Singapore 2023)
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Anomalous random walks and scaling limits: from fractals to random media
(AustMS 2023 at the University of Queensland 2023)
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Anomalous random walks and scaling limits: from fractals to random media
(International Congress of Basic Science at BIMSA (China) 2023)
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Gradient estimates of the heat kernel for random walks in time-dependent random environments
(Potential theory and random walks in metric spaces, OIST 2023)
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On gradient estimates of the heat kernel for random walks in time-dependent random environments
(Spring Probability Workshop National Taiwan University 2023)
more...
Works (20):
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確率モデルの上のランダムウォークの漸近挙動についての研究
2003 - 2004
-
放物型Harnack不等式の安定性に関する研究
2003 - 2004
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飛躍型確率過程の熱核の研究
2003 - 2004
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Asymptotic behaviour of random walks on stochastic models
2003 - 2004
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Stability of parabolic Harnack inequalities on metric measure spaces
2003 - 2004
more...
Education (4):
- - 1991 Kyoto University
- - 1991 Kyoto University Graduate School, Division of Natural Science
- - 1989 Kyoto University Faculty of Science
- - 1989 Kyoto University Faculty of Science
Professional career (1):
- Doctor of Science (Kyoto University)
Work history (3):
- 2022/04 - 現在 Waseda University Faculty of Science and Engineering Professor
- 2010/10 - 2022/03 Kyoto University Research Institute for Mathematical Sciences Professor
- 2007/04 - 2010/09 Kyoto University Graduate School of Science Division of Mathematics Professor
Awards (8):
- 2017/11 - Humboldt Research Award
- 2017/11 - Osaka Science Prize
- 2017/02 - Inoue Prize for Science
- 2012/03 - JSPS (Japan Society for the Promotion of Science) Prize
- 2004 - 日本数学会賞春季賞
- 2004 - Prize of the Mathematical Society of Japan
- 1997 - 日本数学会建部賞
- 1997 - Takebe-Award, Math. Soc. Japan
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Association Membership(s) (2):
Institute of Mathematical Statistics
, Mathematical Society of Japan
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