## Kumagai, Takashi

Compute Distance To:
 Author ID: kumagai.takashi Published as: Kumagai, Takashi; Kumagai, T. External Links: MGP · ORCID · Wikidata
 Documents Indexed: 95 Publications since 1993, including 2 Books 7 Contributions as Editor Co-Authors: 60 Co-Authors with 86 Joint Publications 1,772 Co-Co-Authors
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### Co-Authors

 16 single-authored 21 Chen, Zhen-Qing 17 Wang, Jian 14 Hambly, Ben M. 11 Barlow, Martin T. 9 Croydon, David A. 9 Kim, Panki 8 Bass, Richard F. 7 Chen, Xin 5 Sturm, Karl-Theodor 3 Gordina, Masha 3 Grigor’yan, Alexander Asaturovich 3 Nakamura, Chikara 3 Saloff-Coste, Laurent 2 Can, Van Hao 2 Chen, Guanyu 2 Coulhon, Thierry 2 Hino, Masanori 2 Kassmann, Moritz 2 Kusuoka, Shigeo 1 Aikawa, Hiroaki 1 Arakawa, Tomoyuki 1 Ben Arous, Gérard 1 Bogdan, Krzysztof 1 Boukhadra, Omar 1 Chen, Zhengqing 1 Dembo, Amir 1 Deuschel, Jean-Dominique 1 Fitzsimmons, Patrick J. 1 Franchi, Bruno 1 Fribergh, Alexander 1 Fujii, Ichiro 1 Hasegawa, Masahito 1 Hu, Jiaxin 1 Huang, Ruojun 1 Járai, Antal A. 1 Kashiwara, Masaki 1 Kigami, Jun 1 Kim, Kyung Youn 1 Kotani, Motoko 1 Kwaśnicki, Mateusz 1 Makino, Kazuhisa 1 Mathieu, Pierre 1 Misumi, Jun 1 Mizuta, Yoshihiro 1 Mochizuki, Takuro 1 Mukai, Shigeru 1 Nakajima, Hiraku 1 Nakanishi, Kenji 1 Ono, Kaoru 1 Ozawa, Narutaka 1 Slade, Gordon 1 Suzuki, Noriaki 1 Tamagawa, Akio 1 Teplyaev, Alexander 1 Tomotada, Ohtsuki 1 Uemura, Toshihiro 1 van der Hofstad, Remco W. 1 Yamada, Michio 1 Zeitouni, Ofer 1 Zhou, Xianyin
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### Serials

 9 Probability Theory and Related Fields 6 Electronic Journal of Probability 5 Journal of Functional Analysis 5 Stochastic Processes and their Applications 4 The Annals of Probability 4 Journal of the Mathematical Society of Japan 4 Transactions of the American Mathematical Society 4 Oberwolfach Reports 3 Communications in Mathematical Physics 3 Publications of the Research Institute for Mathematical Sciences, Kyoto University 2 Communications on Pure and Applied Mathematics 2 Journal of Mathematics of Kyoto University 2 Journal of Theoretical Probability 2 Journal de Mathématiques Pures et Appliquées. Neuvième Série 2 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 2 Electronic Communications in Probability 2 Journal of the European Mathematical Society (JEMS) 2 Advanced Studies in Pure Mathematics 2 RIMS Kôkyûroku Bessatsu 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Revue Roumaine de Mathématiques Pures et Appliquées 1 Advances in Mathematics 1 Illinois Journal of Mathematics 1 Journal für die Reine und Angewandte Mathematik 1 Mathematische Annalen 1 Mathematische Zeitschrift 1 Memoirs of the American Mathematical Society 1 Osaka Journal of Mathematics 1 Proceedings of the London Mathematical Society. Third Series 1 Tôhoku Mathematical Journal. Second Series 1 Revista Matemática Iberoamericana 1 Forum Mathematicum 1 The Annals of Applied Probability 1 SIAM Journal on Mathematical Analysis 1 Potential Analysis 1 Kyushu Journal of Mathematics 1 Fractals 1 Bernoulli 1 RIMS Kokyuroku 1 Acta Mathematica Sinica. English Series 1 Lecture Notes in Mathematics 1 ALEA. Latin American Journal of Probability and Mathematical Statistics
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### Fields

 95 Probability theory and stochastic processes (60-XX) 24 Potential theory (31-XX) 20 Measure and integration (28-XX) 15 Partial differential equations (35-XX) 8 Statistical mechanics, structure of matter (82-XX) 7 General and overarching topics; collections (00-XX) 7 Operator theory (47-XX) 6 Global analysis, analysis on manifolds (58-XX) 5 Combinatorics (05-XX) 5 Functional analysis (46-XX) 3 Differential geometry (53-XX) 1 History and biography (01-XX) 1 Algebraic geometry (14-XX) 1 Group theory and generalizations (20-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Ordinary differential equations (34-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Difference and functional equations (39-XX) 1 Integral equations (45-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Geometry (51-XX)

### Citations contained in zbMATH Open

81 Publications have been cited 1,611 times in 774 Documents Cited by Year
Heat kernel estimates for stable-like processes on $$d$$-sets. Zbl 1075.60556
Chen, Zhen-Qing; Kumagai, Takashi
2003
Heat kernel estimates for jump processes of mixed types on metric measure spaces. Zbl 1131.60076
Chen, Zhen-Qing; Kumagai, Takashi
2008
Global heat kernel estimates for symmetric jump processes. Zbl 1234.60088
Chen, Zhen-Qing; Kim, Panki; Kumagai, Takashi
2011
Heat kernel upper bounds for jump processes and the first exit time. Zbl 1158.60039
Barlow, Martin T.; Grigor’yan, Alexander; Kumagai, Takashi
2009
Weighted Poincaré inequality and heat kernel estimates for finite range jump processes. Zbl 1156.60069
Chen, Zhen-Qing; Kim, Panki; Kumagai, Takashi
2008
Stability of parabolic Harnack inequalities on metric measure spaces. Zbl 1102.60064
Barlow, Martin T.; Bass, Richard F.; Kumagai, Takashi
2006
Estimates of transition densities for Brownian motion of nested fractals. Zbl 0792.60073
Kumagai, Takashi
1993
Transition density estimates for Brownian motion on affine nested fractals. Zbl 0853.60062
Fitzsimmons, Pat J.; Hambly, Ben M.; Kumagai, Takashi
1994
Uniqueness of Brownian motion on Sierpiński carpets. Zbl 1200.60070
Barlow, Martin T.; Bass, Richard F.; Kumagai, Takashi; Teplyaev, Alexander
2010
Transition density estimates for diffusion processes on post critically finite self-similar fractals. Zbl 1027.60087
Hambly, B. M.; Kumagai, T.
1999
Characterization of sub-Gaussian heat kernel estimates on strongly recurrent graphs. Zbl 1083.60060
Barlow, Martin T.; Coulhoun, Thierry; Kumagai, Takashi
2005
On the equivalence of parabolic Harnack inequalities and heat kernel estimates. Zbl 1281.58016
Barlow, Martin T.; Grigor’yan, Alexander; Kumagai, Takashi
2012
Random walk on the incipient infinite cluster on trees. Zbl 1110.60090
Barlow, Martin T.; Kumagai, Takashi
2006
Random walks on disordered media and their scaling limits. École d’Été de Probabilités de Saint-Flour XL – 2010. Zbl 1360.60003
Kumagai, Takashi
2014
A priori Hölder estimate, parabolic Harnack principle and heat kernel estimates for diffusions with jumps. Zbl 1200.60065
Chen, Zhen-Qing; Kumagai, Takashi
2010
On heat kernel estimates and parabolic Harnack inequality for jump processes on metric measure spaces. Zbl 1171.60373
Chen, Zhen-Qing; Kim, Panki; Kumagai, Takashi
2009
Random walk on the incipient infinite cluster for oriented percolation in high dimensions. Zbl 1144.82030
Barlow, Martin T.; Járai, Antal A.; Kumagai, Takashi; Slade, Gordon
2008
Boundary Harnack inequality for Markov processes with jumps. Zbl 1309.60080
Bogdan, Krzysztof; Kumagai, Takashi; Kwaśnicki, Mateusz
2015
Symmetric jump processes: localization, heat kernels and convergence. Zbl 1201.60078
Bass, Richard F.; Kassmann, Moritz; Kumagai, Takashi
2010
Heat kernel estimates for strongly recurrent random walk on random media. Zbl 1159.60029
Kumagai, Takashi; Misumi, Jun
2008
Brownian motion penetrating fractals. An application of the trace theorem of Besov spaces. Zbl 0960.31005
Kumagai, Takashi
2000
Construction of diffusion processes on fractals, $$d$$-sets, and general metric measure spaces. Zbl 1086.60052
Kumagai, Takashi; Sturm, Karl-Theodor
2005
Heat kernel estimates and parabolic Harnack inequalities on graphs and resistance forms. Zbl 1067.60070
Kumagai, Takashi
2004
Parabolic Harnack inequality and heat kernel estimates for random walks with long range jumps. Zbl 1159.60021
Barlow, Martin T.; Bass, Richard F.; Kumagai, Takashi
2009
Heat kernel estimates for symmetric random walks on a class of fractal graphs and stability under rough isometries. Zbl 1065.60041
Hambly, Ben M.; Kumagai, Takashi
2004
Diffusion processes on fractal fields: Heat kernel estimates and large deviations. Zbl 1035.60083
Hambly, B. M.; Kumagai, T.
2003
Symmetric Markov chains on $$\mathbb{Z}^d$$ with unbounded range. Zbl 1130.60076
Bass, Richard F.; Kumagai, Takashi
2008
Discrete approximation of symmetric jump processes on metric measure spaces. Zbl 1274.60238
Chen, Zhen-Qing; Kim, Panki; Kumagai, Takashi
2013
Random walks on Galton-Watson trees with infinite variance offspring distribution conditioned to survive. Zbl 1191.60121
Croydon, David A.; Kumagai, Takashi
2008
Some remarks for stable-like jump processes on fractals. Zbl 1029.60067
Kumagai, Takashi
2003
Nash-type inequalities and heat kernels for non-local Dirichlet forms. Zbl 1119.60068
Hu, Jiaxin; Kumagai, Takashi
2006
On the dichotomy in the heat kernel two sided estimates. Zbl 1162.47037
Grigor’yan, Alexander; Kumagai, Takashi
2008
Harnack inequalities and local central limit theorem for the polynomial lower tail random conductance model. Zbl 1332.60065
Boukhadra, Omar; Kumagai, Takashi; Mathieu, Pierre
2015
A trace theorem for Dirichlet forms on fractals. Zbl 1111.47005
Hino, Masanori; Kumagai, Takashi
2006
Heat kernel estimates for time fractional equations. Zbl 1401.60088
Chen, Zhen-Qing; Kim, Panki; Kumagai, Takashi; Wang, Jian
2018
Subsequential scaling limits of simple random walk on the two-dimensional uniform spanning tree. Zbl 1377.60022
Barlow, M. T.; Croydon, D. A.; Kumagai, T.
2017
Laws of the iterated logarithm for the range of random walks in two and three dimensions. Zbl 1031.60031
Bass, Richard F.; Kumagai, Takashi
2002
Diffusion on the scaling limit of the critical percolation cluster in the diamond hierarchical lattice. Zbl 1191.82024
Hambly, B. M.; Kumagai, T.
2010
Transition density estimates for diffusion processes on homogeneous random Sierpiński carpets. Zbl 0962.60078
Hambly, Ben M.; Kumagai, Takashi; Kusuoka, Shigeo; Zhou, Xian Yin
2000
Regularity, closedness and spectral dimensions of the Dirichlet forms on P.C.F. self-similar sets. Zbl 0798.58042
Kumagai, Takashi
1993
Biased random walk on critical Galton-Watson trees conditioned to survive. Zbl 1283.60125
Croydon, D. A.; Fribergh, A.; Kumagai, T.
2013
Elliptic Harnack inequalities for symmetric non-local Dirichlet forms. Zbl 1415.35069
Chen, Zhen-Qing; Kumagai, Takashi; Wang, Jian
2019
Time fractional Poisson equations: representations and estimates. Zbl 1427.35312
Chen, Zhen-Qing; Kim, Panki; Kumagai, Takashi; Wang, Jian
2020
Homogenization of nested fractals. Zbl 0843.31004
Kumagai, T.; Kusuoka, S.
1996
Laws of the iterated logarithm for symmetric jump processes. Zbl 1407.60114
Kim, Panki; Kumagai, Takashi; Wang, Jian
2017
Time-changes of stochastic processes associated with resistance forms. Zbl 1386.60264
Croydon, David; Hambly, Ben; Kumagai, Takashi
2017
Short time asymptotic behaviour and large deviation for Brownian motion on some affine nested fractals. Zbl 0888.60030
Kumagai, Takashi
1997
Heat kernel estimates and homogenization for asymptotically lower dimensional processes on some nested fractals. Zbl 0910.60062
Hambly, B. M.; Kumagai, T.
1998
Convergence of symmetric Markov chains on $${\mathbb{Z}^d}$$. Zbl 1200.60060
Bass, Richard F.; Kumagai, Takashi; Uemura, Toshihiro
2010
Quenched invariance principles for random walks and elliptic diffusions in random media with boundary. Zbl 1338.60098
Chen, Zhen-Qing; Croydon, David A.; Kumagai, Takashi
2015
Recent developments of analysis on fractals. Zbl 1172.28302
Kumagai, Takashi
2008
Construction and some properties of a class of non-symmetric diffusion processes on the Sierpinski gasket. Zbl 0787.60100
Kumagai, T.
1993
Stability and instability of Gaussian heat kernel estimates for random walks among time-dependent conductances. Zbl 1338.60196
Huang, Ruojun; Kumagai, Takashi
2016
Laws of the iterated logarithm for some symmetric diffusion processes. Zbl 0972.60007
Bass, Richard F.; Kumagai, Takashi
2000
Transition density asymptotics for some diffusion processes with multi-fractal structures. Zbl 0974.60061
Barlow, Martin T.; Kumagai, Takashi
2001
Convergence of mixing times for sequences of random walks on finite graphs. Zbl 1244.05207
Croydon, David A.; Hambly, Ben M.; Kumagai, Takashi
2012
Heat kernel estimates on the incipient infinite cluster for critical branching processes. Zbl 1135.60060
Fujii, Ichiro; Kumagai, Takashi
2008
Multifractal formalisms for the local spectral and walk dimensions. Zbl 1002.60064
Hambly, B. M.; Kigami, Jun; Kumagai, Takashi
2002
Function spaces and stochastic processes of fractals. Zbl 1081.60059
Kumagai, Takashi
2004
Large deviations for Brownian motion on the Sierpiński gasket. Zbl 0997.60018
Ben Arous, Gerard; Kumagai, Takashi
2000
Asymptotics for the spectral and walk dimension as fractals approach Euclidean space. Zbl 1075.28003
Hambly, B. M.; Kumagai, T.
2002
Fluctuation of the transition density for Brownian motion on random recursive Sierpiński gaskets. Zbl 1047.60084
Hambly, B. M.; Kumagai, Takashi
2001
Random conductance models with stable-like jumps: heat kernel estimates and Harnack inequalities. Zbl 1459.60213
Chen, Xin; Kumagai, Takashi; Wang, Jian
2020
Stability of parabolic Harnack inequalities for symmetric non-local Dirichlet forms. Zbl 1455.35004
Chen, Zhen-Qing; Kumagai, Takashi; Wang, Jian
2020
Heat kernel estimates and parabolic Harnack inequalities for symmetric Dirichlet forms. Zbl 1471.60118
Chen, Zhen-Qing; Kumagai, Takashi; Wang, Jian
2020
Quenched invariance principle for a class of random conductance models with long-range jumps. Zbl 1472.60059
Biskup, Marek; Chen, Xin; Kumagai, Takashi; Wang, Jian
2021
Corrigendum to: “Global heat kernel estimates for symmetric jump processes”. Zbl 1330.60102
Chen, Zhen-Qing; Kim, Panki; Kumagai, Takashi
2015
Heat kernel estimates for FIN processes associated with resistance forms. Zbl 1422.60129
Croydon, D. A.; Hambly, B. M.; Kumagai, T.
2019
Anomalous random walks and diffusions: from fractals to random media. Zbl 1373.60135
Kumagai, Takashi
2014
Homogenization on finitely ramified fractals. Zbl 1063.60104
Kumagai, Takashi
2004
Lamplighter random walks on fractals. Zbl 1395.60080
Kumagai, Takashi; Nakamura, Chikara
2018
Markov chain approximations to nonsymmetric diffusions with bounded coefficients. Zbl 1278.60118
Deuschel, Jean-Dominique; Kumagai, Takashi
2013
Laws on the iterated logarithm for random walks on random conductance models. Zbl 1367.60023
Kumagai, Takashi; Nakamura, Chikara
2016
Fluctuations of maxima of discrete Gaussian free fields on a class of recurrent graphs. Zbl 1329.60136
Kumagai, Takashi; Zeitouni, Ofer
2013
Stochastic processes on fractals and related topics. Zbl 0943.60072
Kumagai, Takashi
1997
Rotation invariance and characterization of a class of self-similar diffusion processes on the Sierpinski gasket. Zbl 0857.60075
Kumagai, Takashi
1995
Cutoff for lamplighter chains on fractals. Zbl 1410.60070
Dembo, Amir; Kumagai, Takashi; Nakamura, Chikara
2018
Cutoffs for product chains. Zbl 1409.60106
Chen, Guan-Yu; Kumagai, Takashi
2018
Heat kernels, stochastic processes and functional inequalities. Abstracts from the workshop held May 5–11, 2013. Zbl 1349.00173
2013
Homogenization of symmetric stable-like processes in stationary ergodic media. Zbl 1481.60089
Chen, Xin; Chen, Zhen-Qing; Kumagai, Takashi; Wang, Jian
2021
Quenched and averaged tails of the heat kernel of the two-dimensional uniform spanning tree. Zbl 07434397
Barlow, M. T.; Croydon, D. A.; Kumagai, T.
2021
Quenched invariance principle for a class of random conductance models with long-range jumps. Zbl 1472.60059
Biskup, Marek; Chen, Xin; Kumagai, Takashi; Wang, Jian
2021
Homogenization of symmetric stable-like processes in stationary ergodic media. Zbl 1481.60089
Chen, Xin; Chen, Zhen-Qing; Kumagai, Takashi; Wang, Jian
2021
Quenched and averaged tails of the heat kernel of the two-dimensional uniform spanning tree. Zbl 07434397
Barlow, M. T.; Croydon, D. A.; Kumagai, T.
2021
Time fractional Poisson equations: representations and estimates. Zbl 1427.35312
Chen, Zhen-Qing; Kim, Panki; Kumagai, Takashi; Wang, Jian
2020
Random conductance models with stable-like jumps: heat kernel estimates and Harnack inequalities. Zbl 1459.60213
Chen, Xin; Kumagai, Takashi; Wang, Jian
2020
Stability of parabolic Harnack inequalities for symmetric non-local Dirichlet forms. Zbl 1455.35004
Chen, Zhen-Qing; Kumagai, Takashi; Wang, Jian
2020
Heat kernel estimates and parabolic Harnack inequalities for symmetric Dirichlet forms. Zbl 1471.60118
Chen, Zhen-Qing; Kumagai, Takashi; Wang, Jian
2020
Elliptic Harnack inequalities for symmetric non-local Dirichlet forms. Zbl 1415.35069
Chen, Zhen-Qing; Kumagai, Takashi; Wang, Jian
2019
Heat kernel estimates for FIN processes associated with resistance forms. Zbl 1422.60129
Croydon, D. A.; Hambly, B. M.; Kumagai, T.
2019
Heat kernel estimates for time fractional equations. Zbl 1401.60088
Chen, Zhen-Qing; Kim, Panki; Kumagai, Takashi; Wang, Jian
2018
Lamplighter random walks on fractals. Zbl 1395.60080
Kumagai, Takashi; Nakamura, Chikara
2018
Cutoff for lamplighter chains on fractals. Zbl 1410.60070
Dembo, Amir; Kumagai, Takashi; Nakamura, Chikara
2018
Cutoffs for product chains. Zbl 1409.60106
Chen, Guan-Yu; Kumagai, Takashi
2018
Subsequential scaling limits of simple random walk on the two-dimensional uniform spanning tree. Zbl 1377.60022
Barlow, M. T.; Croydon, D. A.; Kumagai, T.
2017
Laws of the iterated logarithm for symmetric jump processes. Zbl 1407.60114
Kim, Panki; Kumagai, Takashi; Wang, Jian
2017
Time-changes of stochastic processes associated with resistance forms. Zbl 1386.60264
Croydon, David; Hambly, Ben; Kumagai, Takashi
2017
Stability and instability of Gaussian heat kernel estimates for random walks among time-dependent conductances. Zbl 1338.60196
Huang, Ruojun; Kumagai, Takashi
2016
Laws on the iterated logarithm for random walks on random conductance models. Zbl 1367.60023
Kumagai, Takashi; Nakamura, Chikara
2016
Boundary Harnack inequality for Markov processes with jumps. Zbl 1309.60080
Bogdan, Krzysztof; Kumagai, Takashi; Kwaśnicki, Mateusz
2015
Harnack inequalities and local central limit theorem for the polynomial lower tail random conductance model. Zbl 1332.60065
Boukhadra, Omar; Kumagai, Takashi; Mathieu, Pierre
2015
Quenched invariance principles for random walks and elliptic diffusions in random media with boundary. Zbl 1338.60098
Chen, Zhen-Qing; Croydon, David A.; Kumagai, Takashi
2015
Corrigendum to: “Global heat kernel estimates for symmetric jump processes”. Zbl 1330.60102
Chen, Zhen-Qing; Kim, Panki; Kumagai, Takashi
2015
Random walks on disordered media and their scaling limits. École d’Été de Probabilités de Saint-Flour XL – 2010. Zbl 1360.60003
Kumagai, Takashi
2014
Anomalous random walks and diffusions: from fractals to random media. Zbl 1373.60135
Kumagai, Takashi
2014
Discrete approximation of symmetric jump processes on metric measure spaces. Zbl 1274.60238
Chen, Zhen-Qing; Kim, Panki; Kumagai, Takashi
2013
Biased random walk on critical Galton-Watson trees conditioned to survive. Zbl 1283.60125
Croydon, D. A.; Fribergh, A.; Kumagai, T.
2013
Markov chain approximations to nonsymmetric diffusions with bounded coefficients. Zbl 1278.60118
Deuschel, Jean-Dominique; Kumagai, Takashi
2013
Fluctuations of maxima of discrete Gaussian free fields on a class of recurrent graphs. Zbl 1329.60136
Kumagai, Takashi; Zeitouni, Ofer
2013
Heat kernels, stochastic processes and functional inequalities. Abstracts from the workshop held May 5–11, 2013. Zbl 1349.00173
2013
On the equivalence of parabolic Harnack inequalities and heat kernel estimates. Zbl 1281.58016
Barlow, Martin T.; Grigor&rsquo;yan, Alexander; Kumagai, Takashi
2012
Convergence of mixing times for sequences of random walks on finite graphs. Zbl 1244.05207
Croydon, David A.; Hambly, Ben M.; Kumagai, Takashi
2012
Global heat kernel estimates for symmetric jump processes. Zbl 1234.60088
Chen, Zhen-Qing; Kim, Panki; Kumagai, Takashi
2011
Uniqueness of Brownian motion on Sierpiński carpets. Zbl 1200.60070
Barlow, Martin T.; Bass, Richard F.; Kumagai, Takashi; Teplyaev, Alexander
2010
A priori Hölder estimate, parabolic Harnack principle and heat kernel estimates for diffusions with jumps. Zbl 1200.60065
Chen, Zhen-Qing; Kumagai, Takashi
2010
Symmetric jump processes: localization, heat kernels and convergence. Zbl 1201.60078
Bass, Richard F.; Kassmann, Moritz; Kumagai, Takashi
2010
Diffusion on the scaling limit of the critical percolation cluster in the diamond hierarchical lattice. Zbl 1191.82024
Hambly, B. M.; Kumagai, T.
2010
Convergence of symmetric Markov chains on $${\mathbb{Z}^d}$$. Zbl 1200.60060
Bass, Richard F.; Kumagai, Takashi; Uemura, Toshihiro
2010
Heat kernel upper bounds for jump processes and the first exit time. Zbl 1158.60039
Barlow, Martin T.; Grigor&rsquo;yan, Alexander; Kumagai, Takashi
2009
On heat kernel estimates and parabolic Harnack inequality for jump processes on metric measure spaces. Zbl 1171.60373
Chen, Zhen-Qing; Kim, Panki; Kumagai, Takashi
2009
Parabolic Harnack inequality and heat kernel estimates for random walks with long range jumps. Zbl 1159.60021
Barlow, Martin T.; Bass, Richard F.; Kumagai, Takashi
2009
Heat kernel estimates for jump processes of mixed types on metric measure spaces. Zbl 1131.60076
Chen, Zhen-Qing; Kumagai, Takashi
2008
Weighted Poincaré inequality and heat kernel estimates for finite range jump processes. Zbl 1156.60069
Chen, Zhen-Qing; Kim, Panki; Kumagai, Takashi
2008
Random walk on the incipient infinite cluster for oriented percolation in high dimensions. Zbl 1144.82030
Barlow, Martin T.; Járai, Antal A.; Kumagai, Takashi; Slade, Gordon
2008
Heat kernel estimates for strongly recurrent random walk on random media. Zbl 1159.60029
Kumagai, Takashi; Misumi, Jun
2008
Symmetric Markov chains on $$\mathbb{Z}^d$$ with unbounded range. Zbl 1130.60076
Bass, Richard F.; Kumagai, Takashi
2008
Random walks on Galton-Watson trees with infinite variance offspring distribution conditioned to survive. Zbl 1191.60121
Croydon, David A.; Kumagai, Takashi
2008
On the dichotomy in the heat kernel two sided estimates. Zbl 1162.47037
Grigor&rsquo;yan, Alexander; Kumagai, Takashi
2008
Recent developments of analysis on fractals. Zbl 1172.28302
Kumagai, Takashi
2008
Heat kernel estimates on the incipient infinite cluster for critical branching processes. Zbl 1135.60060
Fujii, Ichiro; Kumagai, Takashi
2008
Stability of parabolic Harnack inequalities on metric measure spaces. Zbl 1102.60064
Barlow, Martin T.; Bass, Richard F.; Kumagai, Takashi
2006
Random walk on the incipient infinite cluster on trees. Zbl 1110.60090
Barlow, Martin T.; Kumagai, Takashi
2006
Nash-type inequalities and heat kernels for non-local Dirichlet forms. Zbl 1119.60068
Hu, Jiaxin; Kumagai, Takashi
2006
A trace theorem for Dirichlet forms on fractals. Zbl 1111.47005
Hino, Masanori; Kumagai, Takashi
2006
Characterization of sub-Gaussian heat kernel estimates on strongly recurrent graphs. Zbl 1083.60060
Barlow, Martin T.; Coulhoun, Thierry; Kumagai, Takashi
2005
Construction of diffusion processes on fractals, $$d$$-sets, and general metric measure spaces. Zbl 1086.60052
Kumagai, Takashi; Sturm, Karl-Theodor
2005
Heat kernel estimates and parabolic Harnack inequalities on graphs and resistance forms. Zbl 1067.60070
Kumagai, Takashi
2004
Heat kernel estimates for symmetric random walks on a class of fractal graphs and stability under rough isometries. Zbl 1065.60041
Hambly, Ben M.; Kumagai, Takashi
2004
Function spaces and stochastic processes of fractals. Zbl 1081.60059
Kumagai, Takashi
2004
Homogenization on finitely ramified fractals. Zbl 1063.60104
Kumagai, Takashi
2004
Heat kernel estimates for stable-like processes on $$d$$-sets. Zbl 1075.60556
Chen, Zhen-Qing; Kumagai, Takashi
2003
Diffusion processes on fractal fields: Heat kernel estimates and large deviations. Zbl 1035.60083
Hambly, B. M.; Kumagai, T.
2003
Some remarks for stable-like jump processes on fractals. Zbl 1029.60067
Kumagai, Takashi
2003
Laws of the iterated logarithm for the range of random walks in two and three dimensions. Zbl 1031.60031
Bass, Richard F.; Kumagai, Takashi
2002
Multifractal formalisms for the local spectral and walk dimensions. Zbl 1002.60064
Hambly, B. M.; Kigami, Jun; Kumagai, Takashi
2002
Asymptotics for the spectral and walk dimension as fractals approach Euclidean space. Zbl 1075.28003
Hambly, B. M.; Kumagai, T.
2002
Transition density asymptotics for some diffusion processes with multi-fractal structures. Zbl 0974.60061
Barlow, Martin T.; Kumagai, Takashi
2001
Fluctuation of the transition density for Brownian motion on random recursive Sierpiński gaskets. Zbl 1047.60084
Hambly, B. M.; Kumagai, Takashi
2001
Brownian motion penetrating fractals. An application of the trace theorem of Besov spaces. Zbl 0960.31005
Kumagai, Takashi
2000
Transition density estimates for diffusion processes on homogeneous random Sierpiński carpets. Zbl 0962.60078
Hambly, Ben M.; Kumagai, Takashi; Kusuoka, Shigeo; Zhou, Xian Yin
2000
Laws of the iterated logarithm for some symmetric diffusion processes. Zbl 0972.60007
Bass, Richard F.; Kumagai, Takashi
2000
Large deviations for Brownian motion on the Sierpiński gasket. Zbl 0997.60018
Ben Arous, Gerard; Kumagai, Takashi
2000
Transition density estimates for diffusion processes on post critically finite self-similar fractals. Zbl 1027.60087
Hambly, B. M.; Kumagai, T.
1999
Heat kernel estimates and homogenization for asymptotically lower dimensional processes on some nested fractals. Zbl 0910.60062
Hambly, B. M.; Kumagai, T.
1998
Short time asymptotic behaviour and large deviation for Brownian motion on some affine nested fractals. Zbl 0888.60030
Kumagai, Takashi
1997
Stochastic processes on fractals and related topics. Zbl 0943.60072
Kumagai, Takashi
1997
Homogenization of nested fractals. Zbl 0843.31004
Kumagai, T.; Kusuoka, S.
1996
Rotation invariance and characterization of a class of self-similar diffusion processes on the Sierpinski gasket. Zbl 0857.60075
Kumagai, Takashi
1995
Transition density estimates for Brownian motion on affine nested fractals. Zbl 0853.60062
Fitzsimmons, Pat J.; Hambly, Ben M.; Kumagai, Takashi
1994
Estimates of transition densities for Brownian motion of nested fractals. Zbl 0792.60073
Kumagai, Takashi
1993
Regularity, closedness and spectral dimensions of the Dirichlet forms on P.C.F. self-similar sets. Zbl 0798.58042
Kumagai, Takashi
1993
Construction and some properties of a class of non-symmetric diffusion processes on the Sierpinski gasket. Zbl 0787.60100
Kumagai, T.
1993
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### Cited by 658 Authors

 66 Chen, Zhen-Qing 54 Kumagai, Takashi 49 Kim, Panki 34 Song, Renming 31 Wang, Jian 20 Croydon, David A. 19 Teplyaev, Alexander 19 Vondraček, Zoran 18 Grigor’yan, Alexander Asaturovich 18 Hu, Jiaxin 16 Bass, Richard F. 15 Strichartz, Robert S. 13 Barlow, Martin T. 13 Grzywny, Tomasz 13 Hambly, Ben M. 13 Hinz, Michael 13 Kassmann, Moritz 12 Chen, Xin 11 Kaleta, Kamil 10 Andres, Sebastian 9 Deuschel, Jean-Dominique 9 Kuwae, Kazuhiro 9 Lau, Kasing 9 Mimica, Ante 9 Pietruska-Pałuba, Katarzyna 9 Rogers, Luke G. 8 Bogdan, Krzysztof 8 Cao, Shiping 8 Kigami, Jun 8 Murugan, Mathav Kishore 8 Qiu, Hua 8 Schilling, René Leander 8 Shiozawa, Yuichi 8 Uemura, Toshihiro 8 Zähle, Martina 7 Angel, Omer 7 Kajino, Naotaka 7 Masamune, Jun 7 Ryznar, Michał 7 Sztonyk, Paweł 7 Telcs, András 7 Zhang, Xicheng 6 Fukushima, Masatoshi 6 Hutchcroft, Tom 6 Nachmias, Asaf 6 Saloff-Coste, Laurent 6 Slowik, Martin 6 Warma, Mahamadi 6 Xie, Longjie 5 Acuña Valverde, Luis 5 Gu, Qingsong 5 Hino, Masanori 5 Hu, Eryan 5 Kim, Kyung Youn 5 Kwaśnicki, Mateusz 5 Lancia, Maria Rosaria 5 Metz, Volker 5 Neukamm, Stefan 5 Ros-Oton, Xavier 5 Shiraishi, Daisuke 4 Ben Arous, Gérard 4 Bowditch, Adam M. 4 Chen, Xinxing 4 Cho, Soobin 4 Freiberg, Uta Renata 4 Ionescu, Marius V. 4 Kaneko, Hiroshi 4 Kelleher, Daniel J. 4 Kim, Daehong 4 Knopova, Victoria Pavlovna 4 Misumi, Jun 4 Sandrić, Nikola 4 Suzuki, Kohei 4 Szczypkowski, Karol 4 Tarasov, Vasily E. 4 Vernole, Paola Gioia 4 Wada, Masaki 4 Wang, Feng-Yu 4 Wang, Jieming 4 Yan, Litan 4 Yang, Meng 4 Zheng, Tianyi 3 Alonso-Ruiz, Patricia 3 Athreya, Siva R. 3 Bernicot, Frédéric 3 Capitanelli, Raffaela 3 Chen, Xia 3 Chiarini, Alberto 3 da Silva, José Luís 3 Dembo, Amir 3 Ding, Jian 3 Fribergh, Alexander 3 Guan, Qing-Yang 3 Huang, Xueping 3 Jakubowski, Tomasz 3 Járai, Antal A. 3 Jones, Owen Dafydd 3 Keller, Matthias 3 Kim, KyeongHun 3 Kim, Minhyun ...and 558 more Authors
all top 5

### Cited in 155 Serials

 52 Stochastic Processes and their Applications 50 Potential Analysis 45 Probability Theory and Related Fields 42 Journal of Functional Analysis 38 Transactions of the American Mathematical Society 36 The Annals of Probability 25 Journal of Theoretical Probability 24 Communications in Mathematical Physics 22 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 18 Electronic Journal of Probability 13 Journal of Statistical Physics 12 Journal of Mathematical Analysis and Applications 11 Mathematische Zeitschrift 10 Forum Mathematicum 9 Advances in Mathematics 9 Journal of Differential Equations 9 Calculus of Variations and Partial Differential Equations 8 Journal of the Mathematical Society of Japan 7 Journal d’Analyse Mathématique 7 Mathematische Annalen 7 Mathematische Nachrichten 7 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 7 Statistics & Probability Letters 7 Stochastic Analysis and Applications 7 Science China. Mathematics 6 Proceedings of the American Mathematical Society 6 Tôhoku Mathematical Journal. Second Series 6 Journal de Mathématiques Pures et Appliquées. Neuvième Série 6 Bernoulli 6 The Journal of Fourier Analysis and Applications 6 Journal of Evolution Equations 6 Communications on Pure and Applied Analysis 5 Illinois Journal of Mathematics 5 Acta Applicandae Mathematicae 5 Fractals 5 Fractional Calculus & Applied Analysis 5 Stochastics and Dynamics 5 Journal of Fractal Geometry 4 Inventiones Mathematicae 4 Publications of the Research Institute for Mathematical Sciences, Kyoto University 4 Semigroup Forum 4 Communications in Partial Differential Equations 4 SIAM Journal on Mathematical Analysis 4 Electronic Communications in Probability 4 Discrete and Continuous Dynamical Systems 4 Journal of the European Mathematical Society (JEMS) 4 Acta Mathematica Sinica. English Series 4 ALEA. Latin American Journal of Probability and Mathematical Statistics 3 Archive for Rational Mechanics and Analysis 3 Studia Mathematica 3 ZAMP. Zeitschrift für angewandte Mathematik und Physik 3 Journal für die Reine und Angewandte Mathematik 3 Memoirs of the American Mathematical Society 3 Proceedings of the London Mathematical Society. Third Series 3 Zeitschrift für Analysis und ihre Anwendungen 3 Revista Matemática Iberoamericana 3 Science in China. Series A 3 The Annals of Applied Probability 3 The Journal of Geometric Analysis 3 Journal of Mathematical Sciences (New York) 3 NoDEA. Nonlinear Differential Equations and Applications 3 Frontiers of Mathematics in China 3 Discrete and Continuous Dynamical Systems. Series S 3 $$p$$-Adic Numbers, Ultrametric Analysis, and Applications 3 Journal of Spectral Theory 2 Advances in Applied Probability 2 Journal of Mathematical Physics 2 Physics Letters. A 2 Applied Mathematics and Optimization 2 Archiv der Mathematik 2 Duke Mathematical Journal 2 Manuscripta Mathematica 2 Osaka Journal of Mathematics 2 Tokyo Journal of Mathematics 2 Probability and Mathematical Statistics 2 Chinese Annals of Mathematics. Series B 2 Random Structures & Algorithms 2 SIAM Journal on Scientific Computing 2 Applied and Computational Harmonic Analysis 2 Positivity 2 Annals of Mathematics. Second Series 2 Interdisciplinary Information Sciences (IIS) 2 Foundations of Computational Mathematics 2 Communications in Mathematics and Statistics 2 Stochastic and Partial Differential Equations. Analysis and Computations 2 Analysis and Geometry in Metric Spaces 2 Advances in Nonlinear Analysis 1 Applicable Analysis 1 Computers & Mathematics with Applications 1 Communications on Pure and Applied Mathematics 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Letters in Mathematical Physics 1 Lithuanian Mathematical Journal 1 Physica A 1 Rocky Mountain Journal of Mathematics 1 Chaos, Solitons and Fractals 1 Theory of Probability and its Applications 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Collectanea Mathematica ...and 55 more Serials
all top 5

### Cited in 44 Fields

 563 Probability theory and stochastic processes (60-XX) 198 Partial differential equations (35-XX) 163 Potential theory (31-XX) 146 Measure and integration (28-XX) 140 Operator theory (47-XX) 73 Statistical mechanics, structure of matter (82-XX) 66 Combinatorics (05-XX) 42 Functional analysis (46-XX) 28 Global analysis, analysis on manifolds (58-XX) 20 Real functions (26-XX) 20 Quantum theory (81-XX) 18 Harmonic analysis on Euclidean spaces (42-XX) 17 Functions of a complex variable (30-XX) 16 Integral equations (45-XX) 11 Difference and functional equations (39-XX) 9 Dynamical systems and ergodic theory (37-XX) 8 Differential geometry (53-XX) 7 Ordinary differential equations (34-XX) 7 Statistics (62-XX) 6 Convex and discrete geometry (52-XX) 6 General topology (54-XX) 6 Numerical analysis (65-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 5 Fluid mechanics (76-XX) 4 Number theory (11-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Group theory and generalizations (20-XX) 4 Mechanics of deformable solids (74-XX) 3 Approximations and expansions (41-XX) 3 Relativity and gravitational theory (83-XX) 3 Biology and other natural sciences (92-XX) 2 General and overarching topics; collections (00-XX) 2 Topological groups, Lie groups (22-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Abstract harmonic analysis (43-XX) 2 Information and communication theory, circuits (94-XX) 1 Special functions (33-XX) 1 Sequences, series, summability (40-XX) 1 Manifolds and cell complexes (57-XX) 1 Computer science (68-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Geophysics (86-XX) 1 Operations research, mathematical programming (90-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)

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