Alexander Grigorʼyan

Mathematical Physics · 2000–2020

A researcher in the Science corpus: 36 papers; trusts 28 researchers and is trusted by 62 researchers here, as inferred from the citation graph.

Subfields

• Mathematical Physics — 80 citations into it; #628 of 8,562 by trust here, #334 by citations
• Applied Mathematics — 62 citations into it; #276 of 7,620 by trust here, #130 by citations
• Computational Theory and Mathematics — 51 citations into it; #2,373 of 12,182 by trust here, #1,700 by citations
• Geometry and Topology — 25 citations into it; #657 of 7,422 by trust here, #403 by citations
• Statistical and Nonlinear Physics — 11 citations into it
• Statistics and Probability — 10 citations into it; #3,897 of 12,932 by trust here, #3,255 by citations
• Discrete Mathematics and Combinatorics — 5 citations into it

Whom Alexander Grigorʼyan trusts overall

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

1. Martin T. Barlow
2. Jun Kigami
3. Zhen-Qing Chen
4. Richard F. Bass
5. Jiaxin Hu
6. Takashi Kumagai
7. András Telcs
8. L. Saloff‐Coste
9. Yong Lin
10. C. Pittet

Who trusts Alexander Grigorʼyan overall

1. Martin T. Barlow
2. Takashi Kumagai
3. Jiaxin Hu
4. Jun Kigami
5. Zhen-Qing Chen
6. M. Folz
7. Fabrice Baudoin
8. Matthias Keller
9. András Telcs
10. T. Colding

Papers from Alexander Grigorʼyan's perspective

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

1. Harnack inequalities and sub-Gaussian estimates for random walks
2. Non-local dirichlet forms and symmetric jump processes
3. Aspects of Sobolev-type inequalities
4. Transition Probabilities for Symmetric Jump Processes
5. Upper Bounds of Heat Kernels on Doubling Spaces
6. Sub-Gaussian estimates of heat kernels on infinite graphs, to appera in Duke Math
7. Stability of parabolic Harnack inequalities on metric measure spaces
8. On the equivalence of parabolic Harnack inequalities and heat kernel estimates
9. A geometric approach to on-diagonal heat kernel lower bounds on groups
10. Harnack Inequalities for Jump Processes

Their papers

• Heat kernels on metric measure spaces and an application to semilinear elliptic equations (2003) — 180 citations
• Manifolds and graphs with slow heat kernel decay (2001) — 153 citations
• Heat kernel upper bounds for jump processes and the first exit time (2009) — 124 citations
• On stochastic completeness of jump processes (2012) — 94 citations
• Cohomology of digraphs and (undirected) graphs (2015) — 89 citations
• Graphs associated with simplicial complexes (2014) — 60 citations
• Homotopy theory for digraphs (2014) — 134 citations
• Dirichlet heat kernel in the exterior of a compact set (2002) — 80 citations
• Path Complexes and their Homologies (2020) — 116 citations
• On Nonnegative Solutions of the Inequality Δ u + uσ ≤ 0 on Riemannian Manifolds (2014) — 81 citations
• Parabolicity and stochastic completeness of manifolds in terms of the Green formula (2013) — 48 citations
• Introduction to Analysis on Graphs (2018) — 126 citations
• Two-sided estimates of heat kernels of jump type Dirichlet forms (2018) — 52 citations
• Homologies of digraphs and Künneth formulas (2017) — 65 citations
• Kazdan–Warner equation on graph (2016) — 170 citations
• Existence of positive solutions to some nonlinear equations on locally finite graphs (2016) — 140 citations
• Yamabe type equations on graphs (2016) — 191 citations
• Generalized capacity, Harnack inequality and heat kernels of Dirichlet forms on metric measure spaces (2015) — 80 citations
• Heat Kernels on Metric Measure Spaces (2014) — 52 citations
• Estimates of heat kernels for non-local regular Dirichlet forms (2014) — 48 citations