2014 - Fellow of the American Academy of Arts and Sciences
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 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.
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.
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.
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Dimers and amoebae
Richard Kenyon;Andrei Okounkov;Scott Sheffield.
Annals of Mathematics (2006)
A variational principle for domino tilings
Henry Cohn;Henry Cohn;Richard Kenyon;James Propp.
Journal of the American Mathematical Society (2000)
Limit shapes and the complex Burgers equation
Richard W. Kenyon;Andrei Okounkov.
Acta Mathematica (2007)
Dimers and cluster integrable systems
Alexander B. Goncharov;Richard Kenyon.
Annales Scientifiques De L Ecole Normale Superieure (2013)
An introduction to the dimer model
arXiv: Combinatorics (2003)
Dominos and the Gaussian Free Field
Annals of Probability (2001)
Local statistics of lattice dimers
Annales De L Institut Henri Poincare-probabilites Et Statistiques (1997)
Conformal invariance of domino tiling
Annals of Probability (2000)
The Laplacian and Dirac operators on critical planar graphs
Inventiones Mathematicae (2002)
Lectures on Dimers
arXiv: Probability (2009)
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