Anomalous diffusions on disordered media

• Project/Area Number: 17H01093
• Research Category: Grant-in-Aid for Scientific Research (A)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Kyoto University
• Principal Investigator: 熊谷 隆 京都大学, 数理解析研究所, 教授 (90234509)
• Co-Investigator(Kenkyū-buntansha): 相川 弘明 中部大学, 工学部, 教授 (20137889) ; Croydon David 京都大学, 数理解析研究所, 准教授 (50824182) ; 舟木 直久 早稲田大学, 理工学術院, 特任教授 (60112174) ; 福島 竜輝 筑波大学, 数理物質系, 准教授 (60527886) ; 木上 淳 京都大学, 情報学研究科, 教授 (90202035) ; 日野 正訓 京都大学, 理学研究科, 教授 (40303888)
• Project Period (FY): 2017-04-01 – 2022-03-31
• Project Status: Granted (Fiscal Year 2021)
• Budget Amount: ¥43,810,000 (Direct Cost: ¥33,700,000、Indirect Cost: ¥10,110,000); Fiscal Year 2021: ¥8,320,000 (Direct Cost: ¥6,400,000、Indirect Cost: ¥1,920,000); Fiscal Year 2020: ¥10,400,000 (Direct Cost: ¥8,000,000、Indirect Cost: ¥2,400,000); Fiscal Year 2019: ¥9,620,000 (Direct Cost: ¥7,400,000、Indirect Cost: ¥2,220,000); Fiscal Year 2018: ¥7,930,000 (Direct Cost: ¥6,100,000、Indirect Cost: ¥1,830,000); Fiscal Year 2017: ¥7,540,000 (Direct Cost: ¥5,800,000、Indirect Cost: ¥1,740,000)
• Keywords: 確率論 / 複雑系 / 数理物理 / 解析学 / ポテンシャル論 / 統計力学

Outline of Annual Research Achievements

１。熊谷とCroydonは、Barlow氏と共同で二次元一様全域木の上のランダムウォークの熱核評価に現れる振動等の詳細な性質を調べ、さらに熱核のannealedの評価における非対角部分の指数がquenchedのそれと異なることを解明した。熊谷はまた、拡散項とジャンプ項からなる一般の対称確率過程について、対応する熱方程式の解が放物型ハルナック不等式や精密な熱核評価を持つための必要十分条件を導き出した。本研究は、対称拡散過程や飛躍型確率過程の場合に進められてきた安定性理論の統一版であると言える。この結果は、Z.Q. Chen氏とJ. Wang氏との共著論文にまとめ、2020年度に雑誌に掲載された。
２。木上は、自己相似集合の Ahlfors regular conformal dimensionと対応する無限グラフの parabolic index の関係および自己相似集合上への p-energy の構成について研究し、parabolic index とAhlfors regular conformal dimensionの間の不等式などを示した。
３。相川は、intrinsic ultracontractivity の研究を応用して、Lipschitz領域やJohn領域をベースにするシリンダー上の熱方程式の優解の可積分性を与えた。これは正値優調和関数の可積分性に関する結果の放物型拡張である。
４。福島はS. Junk氏と共同で，ランダム媒質中の向きづけられた高分子模型の零温度極限の研究を行い、自由エネルギーの連続性を示した。舟木は、Glauber-零レンジ過程から平均曲率運動の導出を行った。これは非線形な拡散項を経由するため偏微分方程式の観点からも新しい結果である。

Current Status of Research Progress

2: Research has progressed on the whole more than it was originally planned.

Reason

二次元一様全域木の上のランダムウォークの詳細な解析を行うことで、現在の世界的な潮流である「ランダム幾何学」に対して、「ランダム媒質の上の解析学」を展開することができた。複雑度の高いランダム媒質に関する当該研究は、研究代表者や分担者が１５年以上に渡って牽引している分野であるが、SLEなどとも関連して極めて重要なモデルである二次元一様全域木の解析をさらに深めたことは、大きな意義があると考える。また、一般の測度距離空間上の確率過程で、拡散項とジャンプの項を持つものについてDe Giorgi-Nash-Moser理論を構築したことは、熱核評価やHarnack不等式の安定性の観点からも大きな進展であると言える。
代表者や分担者は今年度も国内外での多くの研究集会に招待され、多くの国際共同研究を進めることができた。特に研究代表者は、フンボルト賞受賞の関係でドイツにのべ半年程度滞在し、研究の推進と国際的なネットワークの拡充を行うことができ、２０１９年は充実した一年であった。年度の終わりにコロナ禍のためいくつかの海外渡航を中止せざるを得なくなり、さらに翌年もコロナが続いたため、海外渡航や研究者招聘が全くできなくなったが、Zoomなどのオンラインを通じて共同研究を続ける方法を身につけ、国際共同研究を継続している。

Strategy for Future Research Activity

研究内容に関する方向性はこれまで通りであるが、すでに一年以上、コロナウイルス の影響で海外渡航や外国人招聘が全くできない状況が続いており、この報告書を作成している2021年4月現在（繰越を行ったために報告書の作成が一年ずれている）も変異種が猛威を奮い、先が見えない状況にある。
幸い、この一年間にZoom等のオンラインによる研究交流が確立し、共同研究者とも定期的に連絡をとり、共同研究を順調に進めることができている。オンラインにより、海外のセミナーや研究集会にも京都にいながら参加できるのは便利ではあるが、やはり実際に会って議論することで得られるものには及ばない。
昨年度は、本科研費に関連して開催予定であった国際研究集会はすべて延期となったが、今年度はオンラインハイブリッドによる国際研究集会を開催し、研究拠点としての役割を果たしたいと考えている。その際、国内の若手研究者が積極的に参加できる機会を増やせるよう努めたい。
研究面においては、昨年度は、自宅にいる時間が長くなった分進行中であった共同研究をいくつもまとめ上げることができた。今年度はオンラインでの研究集会でさらに積極的に講演し、また共同研究者とオンラインで密に議論をすることで、新たな研究を切り開いて行く予定である。

Research Products

• [Int'l Joint Research] University of British Columbia(カナダ)
• [Int'l Joint Research] Fujian Normal University/Shianghai Jiao Tong University(中国)
• [Int'l Joint Research] TU-Berlin/TU-Munich(ドイツ)
• [Int'l Joint Research] UCLA/University of Washington(米国)
• [Int'l Joint Research] Universidade Federal do Rio de Janeiro(ブラジル)
• [Int'l Joint Research]
• [Int'l Joint Research] University of British Columbia(カナダ)
• [Int'l Joint Research] Fujian Normal University/Shianghai Jiao Tong University(中国)
• [Int'l Joint Research] TU-Berlin/Weierstrass Institute(ドイツ)
• [Int'l Joint Research] University of Oxford(英国)
• [Int'l Joint Research] Stanford University/UCLA/University of Washington(米国)
• [Int'l Joint Research] University of British Columbia(カナダ)
• [Int'l Joint Research] Stanford University/University of Washington(米国)
• [Int'l Joint Research] University of Oxford/University of Warwick(英国)
• [Int'l Joint Research] Fujian Normal University/Shianghai Jiao Tong University(中国)
• [Int'l Joint Research] Seoul National University(韓国)
• [Journal Article] Time fractional Poisson equations: Representations and estimates (2020)
  • Author(s): Chen Zhen-Qing、Kim Panki、Kumagai Takashi、Wang Jian
  • Journal Title: Journal of Functional Analysis Volume: 278 Pages: 108311-108311
  • DOI: 10.1016/j.jfa.2019.108311
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Biased random walk on the trace of biased random walk on the trace of... (2020)
  • Author(s): D. Croydon and M. Holmes
  • Journal Title: Communications in Mathematical Physics Volume: 375 Pages: 1341-1341
  • DOI: 10.1007/s00220-019-03585-3
  • NAID: 120006878486
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Global integrability of supertemperatures (2020)
  • Author(s): Hiroaki Aikawa, Takanobu Hara, Kentaro Hirata
  • Journal Title: Mathematische Zeitschrift Volume: online Pages: 1049-1063
  • DOI: 10.1007/s00209-020-02467-y
  • Peer Reviewed
• [Journal Article] Heat kernel estimates for FIN processes associated with resistance forms (2019)
  • Author(s): A. Croydon, B.M. Hambly and T. Kumagai
  • Journal Title: Stochastic Processes and their Applications Volume: 129 Pages: 2991-3017
  • DOI: 10.1016/j.spa.2018.08.011
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Elliptic Harnack inequalities for symmetric non-local Dirichlet forms (2019)
  • Author(s): Z.-Q. Chen, T. Kumagai and J. Wang
  • Journal Title: Journal de Mathematiques Pures et Appliques Volume: 125 Pages: 1-42
  • DOI: 10.1016/j.matpur.2017.10.011
  • NAID: 120007147052
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Products of random walks on finite groups with moderate growth (2019)
  • Author(s): Chen Guan-Yu、Kumagai Takashi
  • Journal Title: Tohoku Mathematical Journal Volume: 71 Pages: 281-302
  • DOI: 10.2748/tmj/1561082599
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Motion by Mean Curvature from Glauber-Kawasaki Dynamics (2019)
  • Author(s): Funaki, T., Tsunoda, K.
  • Journal Title: Journal of Statistical Physics Volume: 177 Pages: 183-208
  • DOI: 10.1007/s10955-019-02364-7
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Fast-reaction limit for Glauber-Kawasaki dynamics with two components (2019)
  • Author(s): De Masi A.、Funaki T.、Presutti E.、Vares M. E.
  • Journal Title: Alea (Rio de Janeiro) Volume: 16 Pages: 957-957
  • DOI: 10.30757/alea.v16-34
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Invariant measures in coupled KPZ equations (2019)
  • Author(s): T. Funaki
  • Journal Title: Stochastic Dynamics Out of Equilibrium (Book) Volume: 印刷中 Pages: 560-568
  • DOI: 10.1007/978-3-030-15096-9_20
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Sharp interface limit for stochastically perturbed mass conserving Allen?Cahn equation (2019)
  • Author(s): Funaki Tadahisa、Yokoyama Satoshi
  • Journal Title: Annals of Probability Volume: 47 Pages: 560-612
  • DOI: 10.1214/18-aop1268
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Zero temperature limit for the Brownian directed polymer among Poissonian disasters (2019)
  • Author(s): Fukushima Ryoki、Junk Stefan
  • Journal Title: The Annals of Applied Probability Volume: 29 Pages: 3821-3860
  • DOI: 10.1214/19-aap1493
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Potential theoretic notions related to integrability of superharmonic functions and supertemperatures (2019)
  • Author(s): Hiroaki Aikawa
  • Journal Title: Analysis and Mathematical Physics Volume: 9 Pages: 711-728
  • DOI: 10.1007/s13324-019-00323-9
  • Peer Reviewed
• [Journal Article] Quenched tail estimate for the random walk in random scenery and in random layered conductance (2019)
  • Author(s): Deuschel Jean-Dominique、Fukushima Ryoki
  • Journal Title: Stochastic Processes and their Applications Volume: 129 Pages: 102-128
  • DOI: 10.1016/j.spa.2018.02.011
  • NAID: 120006644057
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Mean value inequalities for jump processes (2018)
  • Author(s): Z.-Q. Chen, T. Kumagai and J. Wang
  • Journal Title: Springer Proc. in Math and Stat. Volume: 229 Pages: 421-437
  • DOI: 10.1007/978-3-319-74929-7_28
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Cutoff for lamplighter chains on fractals (2018)
  • Author(s): A. Dembo, T. Kumagai and C. Nakamura
  • Journal Title: Electronic Journal of Probability Volume: 23 Pages: 1-21
  • DOI: 10.1214/18-ejp196
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Dichotomy of global capacity density in metric measure spaces (2018)
  • Author(s): Aikawa Hiroaki、Bj?rn Anders、Bj?rn Jana、Shanmugalingam Nageswari
  • Journal Title: Advances in Calculus of Variations Volume: 未定 Pages: 387-404
  • DOI: 10.1515/acv-2016-0066
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] An Integrated Version of Varadhan’s Asymptotics for Lower-Order Perturbations of Strong Local Dirichlet Forms (2018)
  • Author(s): Hino Masanori、Matsuura Kouhei
  • Journal Title: Potential Anal. Volume: 48 Pages: 257-300
  • DOI: 10.1007/s11118-017-9634-x
  • NAID: 120006501311
  • Peer Reviewed / Open Access
• [Journal Article] Convergence of a finite volume scheme for a stochastic conservation law involving a Q-Brownian motion (2018)
  • Author(s): T. Funaki, Y. Gao and D. Hilhorst
  • Journal Title: Discrete & Continuous Dynamical Systems - B Volume: 23 Pages: 1459-1502
  • DOI: 10.3934/dcdsb.2018159
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Eigenvalue Fluctuations for Lattice Anderson Hamiltonians: Unbounded Potentials (2018)
  • Author(s): BISKUP Marek、FUKUSHIMA Ryoki、K?NIG Wolfgang
  • Journal Title: IIS Volume: 24 Issue: 1 Pages: 59-76
  • DOI: 10.4036/iis.2018.a.03 10.4036/iis.2018.A.03
  • NAID: 130007412788
  • ISSN: 1340-9050, 1347-6157
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Slowdown estimates for one-dimensional random walks in random environment with holding times (2018)
  • Author(s): Amir Dembo、Ryoki Fukushima、Naoki Kubota
  • Journal Title: Electronic Communications in Probability Volume: 23 Pages: 1-12
  • DOI: 10.1214/18-ecp191
  • NAID: 120006644043
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Scaling limits of stochastic processes associated with resistance forms (2018)
  • Author(s): Croydon David
  • Journal Title: Annales de l'institut Henri Poincare (B) Probabilites et Statistiques Volume: 54 Pages: 1939-1968
  • Peer Reviewed
• [Journal Article] Heat kernel estimates for time fractional equations (2018)
  • Author(s): Z.-Q. Chen, P. Kim, T. Kumagai and J. Wang
  • Journal Title: Forum Mathematicum Volume: 30 Pages: 1163-1192
  • DOI: 10.1515/forum-2017-0192
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Cutoffs for product chains (2018)
  • Author(s): G.-Y. Chen and T. Kumagai
  • Journal Title: Stochastic Processes and their Applications Volume: 128 Pages: 3840-3879
  • DOI: 10.1016/j.spa.2018.01.002
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Time-changes of stochastic processes associated with resistance forms (2017)
  • Author(s): D.A. Croydon, B.M. Hambly and T. Kumagai
  • Journal Title: Electronic Journal of Probability Volume: no. 82 Pages: 1-41
  • DOI: 10.1214/17-ejp99
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Indices of Dirichlet forms. (2017)
  • Author(s): M. Hino
  • Journal Title: Sugaku Expositions Volume: 30 Pages: 187-205
  • DOI: 10.1090/suga/423
  • NAID: 130006882590
  • Int'l Joint Research
• [Journal Article] A coupled KPZ equation, its two types of approximations and existence of global solutions (2017)
  • Author(s): T. Funaki and M. Hoshino
  • Journal Title: Journal of Functional Analysis Volume: 273 Pages: 1165-1204
  • DOI: 10.1016/j.jfa.2017.05.002
  • Peer Reviewed / Int'l Joint Research
• [Presentation] Global integrability of supertemperatures and intrinsic ultracontractivity (2020)
  • Author(s): Aikawa Hiroaki
  • Organizer: Analysis Seminar, University College Dublin
  • Invited
• [Presentation] Homogenization of (symmetric) stable-like processes in random media (2019)
  • Author(s): Kumagai Takashi
  • Organizer: 2019 Spring Probability Workshop at Academia Sinica
  • Int'l Joint Research / Invited
• [Presentation] Heat kernel estimates and parabolic Harnack inequalities for symmetric Dirichlet forms (2019)
  • Author(s): Kumagai Takashi
  • Organizer: Walking through the Brownian Zoo
  • Int'l Joint Research / Invited
• [Presentation] Anomalous random walk and diffusion in random media (2019)
  • Author(s): Kumagai Takashi
  • Organizer: Berlin Mathematical school (BMS) Friday Colloquium
  • Invited
• [Presentation] Stability of heat kernel estimates and parabolic Harnack inequalities for symmetric Dirichlet forms (2019)
  • Author(s): Kumagai Takashi
  • Organizer: Japanese-German Open Conference on Stochastic Analysis 2019
  • Int'l Joint Research / Invited
• [Presentation] Anomalous random walk and diffusion: from fractals to random media (2019)
  • Author(s): Kumagai Takashi
  • Organizer: 50 Years of Mathematics in Bielefeld
  • Int'l Joint Research / Invited
• [Presentation] Mean curvature interface limit from Glauber-Zero range interacting particles (2019)
  • Author(s): Funaki Tadahisa
  • Organizer: Japanese-German Open Conference on Stochastic Analysis 2019
  • Int'l Joint Research / Invited
• [Presentation] Large deviation for lozenge tiling dynamics (2019)
  • Author(s): Funaki Tadahisa
  • Organizer: Large Scale Stochastic Dynamics, Oberwolfach
  • Int'l Joint Research / Invited
• [Presentation] Quenched and averaged tails of the heat kernel of the two-dimensional uniform spanning tree (2019)
  • Author(s): Croydon David
  • Organizer: 41st Stochastic Processes and Their Applications
  • Int'l Joint Research / Invited
• [Presentation] Scaling limits of random walks on random graphs in critical regimes (2019)
  • Author(s): Croydon David
  • Organizer: 日本数学会秋季総合分科会
  • Invited
• [Presentation] Zero temperature limit for directed polymers in random environment (2019)
  • Author(s): Fukushima Ryoki
  • Organizer: Stochastic Analysis, Random Fields, and Integrable Probability
  • Int'l Joint Research / Invited
• [Presentation] Random walks among Bernoulli obstacles (2019)
  • Author(s): Fukushima Ryoki
  • Organizer: CIRM Workshop "Self-interacting Random Walks, Polymers and Folding"
  • Int'l Joint Research / Invited
• [Presentation] Weakly exponential measures and time changes of the Brownian motion (2019)
  • Author(s): Kigami Jun
  • Organizer: IPAM Workshop, Analysis and Geometry of Random Shapes
  • Int'l Joint Research / Invited
• [Presentation] Ahlfors conformal dimension of a metric space and parabolic index of an infinite graph (2019)
  • Author(s): Kigami Jun
  • Organizer: International Conference on Analysis and PDEs on Manifolds and Fractals
  • Int'l Joint Research / Invited
• [Presentation] 複雑シリンダー上の熱方程式の正値優解の可積分性 (2019)
  • Author(s): Aikawa Hiroaki
  • Organizer: 早稲田大学応用解析研究会
  • Invited
• [Presentation] Weakly exponential measures and time changes of the Brownian motion (2019)
  • Author(s): Kigami Jun
  • Organizer: Analysis and Geometry of Random Shapes
  • Int'l Joint Research / Invited
• [Presentation] Quenched invariance principle for random walks among random conductances with stable-like jumps (2018)
  • Author(s): Kumagai Takashi
  • Organizer: Interplay of Random Media and Stochastic Interface Models
  • Int'l Joint Research / Invited
• [Presentation] Quenched invariance principle for random walks among random conductances with stable-like jumps (2018)
  • Author(s): Kumagai Takashi
  • Organizer: Montreal Summer Workshop on Challenges in Probability and Mathematical Physics at CRM
  • Int'l Joint Research / Invited
• [Presentation] Homogenization of symmetric stable-like processes in random media (2018)
  • Author(s): Kumagai Takashi
  • Organizer: Advances in Asymptotic Probability
  • Int'l Joint Research / Invited
• [Presentation] Quenched invariance principle for random walks among random conductances with stable-like jumps (2018)
  • Author(s): Kumagai Takashi
  • Organizer: Non Standard Diffusions in Fluids, Kinetic Equations and Probability at CIRM
  • Int'l Joint Research / Invited
• [Presentation] Global integrability of supertemperatures (2018)
  • Author(s): Aikawa Hiroaki
  • Organizer: International Conference on Complex Analysis, Potential Theory and Applications
  • Int'l Joint Research / Invited
• [Presentation] Parabolic and Elliptic Boundary Behavior on a Non-Smooth Domain (2018)
  • Author(s): Aikawa Hiroaki
  • Organizer: The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications
  • Int'l Joint Research / Invited
• [Presentation] Global integrability of supertemperatures and related notions in potential theory (2018)
  • Author(s): Aikawa Hiroaki
  • Organizer: The 13th HU and SNU Symposium on Mathematics，Probability and Functional Analysis
  • Int'l Joint Research / Invited
• [Presentation] Some properties of energy measures on the Sierpinski gasket (2018)
  • Author(s): Hino Masanori
  • Organizer: 2nd Hong Kong/Kyoto Workshop on ``Fractal Geometry and Related Areas''
  • Int'l Joint Research / Invited
• [Presentation] Asymptotics of integrated Betti numbers for random simplicial complex processes (2018)
  • Author(s): Hino Masanori
  • Organizer: Fractal Geometry and Stochastics 6
  • Int'l Joint Research / Invited
• [Presentation] Motion by mean curvature from Glauber-Kawasaki dynamics (2018)
  • Author(s): Funaki Tadahisa
  • Organizer: Workshop on Interplay of Random Media and Stochastic Interface Models
  • Int'l Joint Research / Invited
• [Presentation] Derivation of coupled KPZ equation from multi-color zero-range process (2018)
  • Author(s): Funaki Tadahisa
  • Organizer: Workshop on Stochastic partial differential equations and related topics
  • Int'l Joint Research / Invited
• [Presentation] Hydrodynamic limit for exclusion processes (2018)
  • Author(s): Funaki Tadahisa
  • Organizer: KAIST Summer School in Probability 2018
  • Int'l Joint Research / Invited
• [Presentation] Geometry of the random walk range conditioned on survival among Bernoulli obstacles (2018)
  • Author(s): Fukushima Ryoki
  • Organizer: Interplay of Random Media and Stochastic Interface Models
  • Int'l Joint Research / Invited
• [Presentation] Zero temperature limit for Brownian directed polymer in Poisonnian disasters (2018)
  • Author(s): Fukushima Ryoki
  • Organizer: 9th International Conference on Stochastic Analysis and its Applications
  • Int'l Joint Research / Invited
• [Presentation] Tail estimates for the random walk in random scenery (2018)
  • Author(s): Fukushima Ryoki
  • Organizer: Gaussian Free Fields and Related Topics
  • Int'l Joint Research / Invited
• [Presentation] Scaling limits and heat kernel estimates for stochastic processes associated with resistance forms (2018)
  • Author(s): Croydon David
  • Organizer: 2nd Hong Kong/Kyoto Workshop on ``Fractal Geometry and Related Areas''
  • Int'l Joint Research / Invited
• [Presentation] Random walks on fractals and critical random graphs: Scaling limits, time-changes and heat kernel estimates (2018)
  • Author(s): Croydon David
  • Organizer: 9th International Conference on Stochastic Analysis and its Applications
  • Int'l Joint Research / Invited
• [Presentation] Scaling limits of stochastic processes associated with resistance forms (2018)
  • Author(s): Croydon David
  • Organizer: Fractal Geometry and Stochastics 6
  • Int'l Joint Research / Invited
• [Presentation] Capacitary width and its applications to parabolic and elliptic boundary behavior (2018)
  • Author(s): H. Aikawa
  • Organizer: London Analysis and Probability Seminar (Imperial College, UK)
  • Invited
• [Presentation] Time changes of stochastic processes: Convergence and heat kernel estimates (2017)
  • Author(s): T. Kumagai
  • Organizer: Random walks with memory at CIRM
  • Int'l Joint Research / Invited
• [Presentation] Convergence of random walks for trap models on disordered media (2017)
  • Author(s): T. Kumagai
  • Organizer: Dynamics, aging and universality in complex systems, NYU
  • Int'l Joint Research / Invited
• [Presentation] Potential theory for symmetric jump processes and applications (2017)
  • Author(s): T. Kumagai
  • Organizer: SPA 2017 in Moscow (Plenary talk)
  • Int'l Joint Research / Invited
• [Presentation] Heat kernel estimates for time fractional equations (2017)
  • Author(s): T. Kumagai
  • Organizer: 13th Workshop on Markov Processes and Related Topics at Wuhan
  • Int'l Joint Research / Invited
• [Presentation] Dichotomy of global capacity density (2017)
  • Author(s): H. Aikawa
  • Organizer: Probability and Analysis 2017 (Banach Center, Poland)
  • Int'l Joint Research / Invited
• [Presentation] Dichotomy of global capacity density (2017)
  • Author(s): H. Aikawa
  • Organizer: Complex and Harmonic Analysis III (Holon Institute of Technology, Israel)
  • Int'l Joint Research / Invited
• [Presentation] Ahlfors regular conformal dimension and critical value of p-energies of a compact metric space (2017)
  • Author(s): J. Kigami
  • Organizer: 1134th AMS Sectional Meeting
  • Int'l Joint Research / Invited
• [Presentation] Asymptotic behavior of lifetime sums for random simplicial complex processes (2017)
  • Author(s): M. Hino
  • Organizer: Japanese--German Open Conference on Stochastic Analysis 2017
  • Int'l Joint Research / Invited
• [Presentation] ランダム複体過程における生存時間和の漸近挙動 (2017)
  • Author(s): 日野正訓
  • Organizer: ディリクレ形式と対称マルコフ過程
  • Invited
• [Presentation] A stochastically perturbed volume preserving mean curvature motion (2017)
  • Author(s): T. Funaki
  • Organizer: International Conference on Mathematical Biology
  • Int'l Joint Research / Invited
• [Presentation] Volume preserving mean curvature flow with stochastic term (2017)
  • Author(s): T. Funaki
  • Organizer: International Workshop on the Multi-Phase Flow; Analysis, Modeling and Numerics
  • Int'l Joint Research / Invited
• [Presentation] Slowdown estimate for the random hopping time dynamics (2017)
  • Author(s): R. Fukushima
  • Organizer: Large scale properties of partial differential equations with random coefficients
  • Int'l Joint Research / Invited
• [Presentation] Quenched tail estimate for the random walk in random scenery (2017)
  • Author(s): R. Fukushima
  • Organizer: Recent Progress in Probability Theory and Its Applications
  • Int'l Joint Research / Invited
• [Book] 確率偏微分方程式 (2019)
  • Author(s): 舟木 直久、乙部 厳己、謝 賓
  • Total Pages: 350
  • Publisher: 岩波書店
  • ISBN: 9784000298254
• [Remarks] Takashi Kumagai's home page
  • URL: http://www.kurims.kyoto-u.ac.jp/~kumagai/kumpre.html
• [Funded Workshop] 1st China-Japan-Korea Joint Probability Workshop (2019)
• [Funded Workshop] Heat Kernels, Stochastic Processes and Functional Inequalities (Oberwolfach Workshop) (2019)
• [Funded Workshop] Gaussian Free Fields and Related Topics (2018)
• [Funded Workshop] Large scale properties of partial differential equations with random coefficients (2017)
• [Funded Workshop] Stochastic Analysis on Large Scale Interacting Systems (2017)