Martin T. Barlow

Applied Mathematics · 2000–2017

A researcher in the Science corpus: 16 papers; trusts 33 researchers and is trusted by 55 researchers here, as inferred from the citation graph.

Subfields

• Applied Mathematics — 65 citations into it; #338 of 7,620 by trust here, #218 by citations
• Mathematical Physics — 58 citations into it; #328 of 8,562 by trust here, #334 by citations
• Geometry and Topology — 34 citations into it; #493 of 7,422 by trust here, #763 by citations
• Statistics and Probability — 18 citations into it; #1,617 of 12,932 by trust here, #2,693 by citations
• Computational Theory and Mathematics — 16 citations into it; #1,364 of 12,182 by trust here, #1,212 by citations
• Condensed Matter Physics — 9 citations into it
• Statistical and Nonlinear Physics — 9 citations into it; #4,988 of 10,127 by trust here, #6,727 by citations
• Finance — 8 citations into it; #8,647 of 10,518 by trust here, #9,725 by citations

Whom Martin T. Barlow trusts overall

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

1. Alexander Grigorʼyan
2. Richard F. Bass
3. Zhen-Qing Chen
4. Takashi Kumagai
5. András Telcs
6. L. Saloff‐Coste
7. Pierre Mathieu
8. M. Hino
9. T. Coulhon
10. Jun Kigami

Who trusts Martin T. Barlow overall

1. Alexander Grigorʼyan
2. Zhen-Qing Chen
3. Takashi Kumagai
4. Jiaxin Hu
5. M. Folz
6. Richard F. Bass
7. M. Kassmann
8. Vladas Sidoravicius
9. P. Garain
10. S. Andres

Papers from Martin T. Barlow's perspective

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

1. Aspects of Sobolev-type inequalities
2. Harnack inequalities and sub-Gaussian estimates for random walks
3. Non-local dirichlet forms and symmetric jump processes
4. Transition Probabilities for Symmetric Jump Processes
5. Harnack Inequalities for Jump Processes
6. Harnack inequality for some classes of Markov processes
7. Sobolev met Poincaré
8. Markov Processes and Potential Theory
9. Stability of parabolic Harnack inequalities
10. Upper Bounds of Heat Kernels on Doubling Spaces

Their papers

• Non-local dirichlet forms and symmetric jump processes (2006) — 296 citations
• The Liouville Property and a Conjecture of De Giorgi (2000) — 159 citations
• Manifolds and graphs with slow heat kernel decay (2001) — 153 citations
• Random walks on supercritical percolation clusters (2003) — 248 citations
• Degenerate stochastic differential equations and super-Markov chains (2002) — 65 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
• Random Walks and Heat Kernels on Graphs (2017) — 141 citations
• Stability of elliptic Harnack inequality (2016) — 47 citations
• Energy inequalities for cutoff functions and some applications (2012) — 67 citations
• On the equivalence of parabolic Harnack inequalities and heat kernel estimates (2012) — 106 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
• Which values of the volume growth and escape time exponent are possible for a graph (2004) — 104 citations
• Stability of parabolic Harnack inequalities (2003) — 123 citations