Takashi Kumagai

Applied Mathematics · 2000–2016

A researcher in the Science corpus: 20 papers; trusts 32 researchers and is trusted by 47 researchers here, as inferred from the citation graph.

Subfields

• Applied Mathematics — 114 citations into it; #347 of 7,620 by trust here, #234 by citations
• Mathematical Physics — 91 citations into it; #244 of 8,562 by trust here, #151 by citations
• Computational Theory and Mathematics — 59 citations into it; #614 of 12,182 by trust here, #822 by citations
• Finance — 36 citations into it; #4,927 of 10,518 by trust here, #4,482 by citations
• Geometry and Topology — 25 citations into it; #2,160 of 7,422 by trust here, #1,803 by citations
• Statistics and Probability — 22 citations into it; #6,035 of 12,932 by trust here, #3,893 by citations
• Statistical and Nonlinear Physics — 12 citations into it
• Control and Systems Engineering — 5 citations into it

Whom Takashi Kumagai trusts overall

Their strongest outbound trust, strongest first, inferred from their citations.

1. Alexander Grigorʼyan
2. Zhen-Qing Chen
3. Martin T. Barlow
4. Richard F. Bass
5. András Telcs
6. Jiaxin Hu
7. Vassili N. Kolokoltsov
8. David A. Levin
9. L. Saloff‐Coste
10. M. Kassmann

Who trusts Takashi Kumagai overall

1. Zhen-Qing Chen
2. Alexander Grigorʼyan
3. Panki Kim
4. M. Kassmann
5. Martin T. Barlow
6. T. Grzywny
7. Ante Mimica
8. Renming Song
9. Jiaxin Hu
10. Richard F. Bass

Papers from Takashi Kumagai's perspective

Ordered by how strongly the researchers Takashi Kumagai trusts endorse each paper. Same corpus, a different order for every researcher.

1. Harnack Inequalities for Jump Processes
2. Non-local dirichlet forms and symmetric jump processes
3. Transition Probabilities for Symmetric Jump Processes
4. Aspects of Sobolev-type inequalities
5. Harnack inequalities and sub-Gaussian estimates for random walks
6. Harnack inequality for some classes of Markov processes
7. Hölder Continuity of Harmonic Functions with Respect to Operators of Variable Order
8. Markov Processes and Potential Theory
9. Heat kernel estimates for stable-like processes on d-sets
10. On the equivalence of parabolic Harnack inequalities and heat kernel estimates

Their papers

• Heat kernel estimates for stable-like processes on d-sets (2003) — 460 citations
• Weighted Poincaré inequality and heat kernel estimates for finite range jump processes (2008) — 107 citations
• A priori Holder estimate, parabolic Harnack principle and heat kernel estimates for diffusions with jumps (2008) — 102 citations
• Boundary Harnack inequality for Markov processes with jumps (2012) — 78 citations
• Construction of diffusion processes on fractals, $d$-sets, and general metric measure spaces (2005) — 71 citations
• Heat kernel upper bounds for jump processes and the first exit time (2009) — 124 citations
• Uniqueness of Brownian motion on Sierpinski carpets (2008) — 154 citations
• Stability of parabolic Harnack inequalities for symmetric non-local Dirichlet forms (2016) — 51 citations
• Stability of heat kernel estimates for symmetric non-local Dirichlet forms (2016) — 59 citations
• On the equivalence of parabolic Harnack inequalities and heat kernel estimates (2012) — 106 citations
• Corrigendum to “Global heat kernel estimates for symmetric jump processes” (2011) — 124 citations
• On heat kernel estimates and parabolic Harnack inequality for jump processes on metric measure spaces (2009) — 71 citations
• Heat kernel estimates for jump processes of mixed types on metric measure spaces (2007) — 329 citations
• Parabolic Harnack inequality and heat kernel estimates for random walks with long range jumps (2007) — 57 citations
• Stability of parabolic Harnack inequalities on metric measure spaces (2006) — 160 citations
• Characterization of sub‐Gaussian heat kernel estimates on strongly recurrent graphs (2005) — 130 citations
• Heat Kernel Estimates and Parabolic Harnack Inequalities on Graphs and Resistance Forms (2004) — 61 citations
• Heat kernel estimates for symmetric random walks on a class of fractal graphs and stability under rough isometries (2003) — 56 citations
• Brownian Motion Penetrating Fractals: An Application of the Trace Theorem of Besov Spaces (2000) — 67 citations
• Transition density estimates for diffusion processes on homogeneous random Sierpinski carpets (2000) — 49 citations