D-Index & Metrics Best Publications

D-Index & Metrics

Discipline name D-index D-index (Discipline H-index) only includes papers and citation values for an examined discipline in contrast to General H-index which accounts for publications across all disciplines. Citations Publications World Ranking National Ranking
Mathematics D-index 37 Citations 6,021 83 World Ranking 1277 National Ranking 564

Research.com Recognitions

Awards & Achievements

2014 - Fellow of the American Academy of Arts and Sciences

Overview

What is he best known for?

The fields of study he is best known for:

  • Geometry
  • Mathematical analysis
  • Combinatorics

Richard Kenyon mainly investigates Combinatorics, Mathematical analysis, Planar graph, Geometry and Laplacian matrix. His biological study spans a wide range of topics, including Arrangement of lines and Theoretical physics. His Boundary value problem, Harnack's inequality, Amoeba and Lipschitz continuity study, which is part of a larger body of work in Mathematical analysis, is frequently linked to De Rham curve, bridging the gap between disciplines.

His work in Planar graph tackles topics such as Spanning tree which are related to areas like Harmonic function, Dirac operator, Logarithm and Lattice. His work carried out in the field of Geometry brings together such families of science as Vertex and Hamiltonian. The various areas that Richard Kenyon examines in his Laplacian matrix study include Heterogeneous random walk in one dimension, Loop-erased random walk and Generalization.

His most cited work include:

  • Dimers and amoebae (401 citations)
  • A variational principle for domino tilings (297 citations)
  • Limit shapes and the complex Burgers equation (214 citations)

What are the main themes of his work throughout his whole career to date?

His primary areas of study are Combinatorics, Discrete mathematics, Planar graph, Spanning tree and Bipartite graph. Richard Kenyon interconnects Matrix and Plane in the investigation of issues within Combinatorics. His work deals with themes such as Arrangement of lines, Square tiling and Hausdorff dimension, which intersect with Discrete mathematics.

His Planar graph study incorporates themes from Bijection, Harmonic function, Conformal symmetry and Surface. Richard Kenyon combines subjects such as Laplacian matrix, Laplace operator, Vertex, Loop-erased random walk and Minimum spanning tree with his study of Spanning tree. His study looks at the intersection of Bipartite graph and topics like Torus with Characteristic polynomial.

He most often published in these fields:

  • Combinatorics (72.18%)
  • Discrete mathematics (23.31%)
  • Planar graph (20.30%)

What were the highlights of his more recent work (between 2014-2021)?

  • Combinatorics (72.18%)
  • Phase transition (7.52%)
  • Graph (8.27%)

In recent papers he was focusing on the following fields of study:

His primary areas of investigation include Combinatorics, Phase transition, Graph, Planar graph and Random graph. His Combinatorics research incorporates themes from Discrete mathematics and Probability measure. His primary area of study in Discrete mathematics is in the field of Bipartite graph.

His research in Phase transition intersects with topics in Phase space, Statistical physics, Exponential function, Entropy and Scaling. In general Graph study, his work on Chromatic polynomial often relates to the realm of Rational mapping, thereby connecting several areas of interest. His Spanning tree research integrates issues from Green's function, Inverse, Square lattice, Loop-erased random walk and Laplace operator.

Between 2014 and 2021, his most popular works were:

  • Bipolar orientations on planar maps and SLE 12 (37 citations)
  • Multipodal Structure and Phase Transitions in Large Constrained Graphs (33 citations)
  • Double-dimers, the Ising model and the hexahedron recurrence (32 citations)

In his most recent research, the most cited papers focused on:

  • Geometry
  • Mathematical analysis
  • Combinatorics

Richard Kenyon mainly focuses on Combinatorics, Phase transition, Vertex model, Schramm–Loewner evolution and Phase space. His Combinatorics study frequently intersects with other fields, such as Scaling. Richard Kenyon works mostly in the field of Scaling, limiting it down to topics relating to Spanning tree and, in certain cases, Scaling limit.

His Vertex model research incorporates elements of Analytic function, Mathematical analysis, Monotone polygon, Parameterized complexity and Grid. His research integrates issues of Statistical mechanics, Mathematical physics, Peano axioms, Invariant and Square in his study of Schramm–Loewner evolution. His work in Phase space addresses issues such as Classification of discontinuities, which are connected to fields such as Random graph.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

Best Publications

Dimers and amoebae

Richard Kenyon;Andrei Okounkov;Scott Sheffield.
Annals of Mathematics (2006)

401 Citations

A variational principle for domino tilings

Henry Cohn;Henry Cohn;Richard Kenyon;James Propp.
Journal of the American Mathematical Society (2000)

297 Citations

An introduction to the dimer model

Richard Kenyon.
arXiv: Combinatorics (2003)

236 Citations

Dominos and the Gaussian Free Field

Richard Kenyon.
Annals of Probability (2001)

214 Citations

Limit shapes and the complex Burgers equation

Richard W. Kenyon;Andrei Okounkov.
Acta Mathematica (2007)

214 Citations

Local statistics of lattice dimers

Richard Kenyon.
Annales De L Institut Henri Poincare-probabilites Et Statistiques (1997)

209 Citations

Lectures on Dimers

Richard Kenyon.
arXiv: Probability (2009)

207 Citations

The Laplacian and Dirac operators on critical planar graphs

R. Kenyon.
Inventiones Mathematicae (2002)

205 Citations

Conformal invariance of domino tiling

Richard Kenyon.
Annals of Probability (2000)

198 Citations

Dimers and cluster integrable systems

Alexander B. Goncharov;Richard Kenyon.
Annales Scientifiques De L Ecole Normale Superieure (2013)

196 Citations

Best Scientists Citing Richard Kenyon

Alexander I. Bobenko

Alexander I. Bobenko

Technical University of Berlin

Publications: 32

Alexei Borodin

Alexei Borodin

MIT

Publications: 25

Boris Solomyak

Boris Solomyak

Bar-Ilan University

Publications: 20

Masahito Yamazaki

Masahito Yamazaki

Kavli Institute for the Physics and Mathematics of the Universe

Publications: 20

Yang-Hui He

Yang-Hui He

City, University of London

Publications: 19

Andrei Okounkov

Andrei Okounkov

Columbia University

Publications: 18

Scott Sheffield

Scott Sheffield

MIT

Publications: 17

Oded Schramm

Oded Schramm

Microsoft (United States)

Publications: 16

Ka-Sing Lau

Ka-Sing Lau

Chinese University of Hong Kong

Publications: 15

David B. Wilson

David B. Wilson

Washington University in St. Louis

Publications: 14

Patrik L. Ferrari

Patrik L. Ferrari

University of Bonn

Publications: 13

Gregory F. Lawler

Gregory F. Lawler

University of Chicago

Publications: 13

Yang Wang

Yang Wang

Hong Kong University of Science and Technology

Publications: 12

Geoffrey Grimmett

Geoffrey Grimmett

University of Cambridge

Publications: 12

Helmut Pottmann

Helmut Pottmann

King Abdullah University of Science and Technology

Publications: 12

Klaus Schmidt

Klaus Schmidt

University of Vienna

Publications: 11

Profile was last updated on December 6th, 2021.
Research.com Ranking is based on data retrieved from the Microsoft Academic Graph (MAG).
The ranking d-index is inferred from publications deemed to belong to the considered discipline.

If you think any of the details on this page are incorrect, let us know.

Contact us
Something went wrong. Please try again later.