344 citations · 1.3k across the 59 of their papers we have counts for
10 papers · 1 filter
Dimers and Circle patterns
Richard Kenyon, Wai Yeung Lam, Sanjay Ramassamy +1
We establish a correspondence between the dimer model on a bipartite graph and a circle pattern with the combinatorics of that graph, which holds for graphs that are either planar…
On the asymptotics of dimers on tori
Richard W. Kenyon, Nike Sun, David B. Wilson
We study asymptotics of the dimer model on large toric graphs. Let be a weighted -periodic planar graph, and let be a large-index sublatt…
Double-dimers, the Ising model and the hexahedron recurrence
Richard Kenyon, Robin Pemantle
We define and study a recurrence relation in , called the hexahedron recurrence, which is similar to the octahedron recurrence (Hirota bilinear difference equation)…
Height fluctuations in the honeycomb dimer model
Richard Kenyon
We study a model of random surfaces arising in the dimer model on the honeycomb lattice. For a fixed ``wire frame'' boundary condition, as the lattice spacing , Cohn, Kenyon…
Dimers and Amoebae
Richard Kenyon, Andrei Okounkov, Scott Sheffield
We study random surfaces which arise as height functions of random perfect matchings (a.k.a. dimer configurations) on an weighted, bipartite, doubly periodic graph G embedded in th…
Rhombic embeddings of planar graphs with faces of degree 4
Richard Kenyon, Jean-Marc Schlenker
Given a finite or infinite planar graph all of whose faces have degree 4, we study embeddings in the plane in which all edges have length 1, that is, in which every face is a rhomb…