128 citations · 165 across the 5 of their papers we have counts for
9 papers
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…
Planar dimers and Harnack curves
Richard Kenyon, Andrei Okounkov
In this paper we study the connection between dimers and Harnack curves discovered in math-ph/0311005. We prove that every Harnack curve arises as a spectral curve of some dimer mo…
An introduction to the dimer model
Richard Kenyon
Lecture notes from a minicourse given at the ICTP in May 2002.
Dimers, Tilings and Trees
Richard Kenyon, Scott Sheffield
Generalizing results of Temperley, Brooks, Smith, Stone and Tutte and others we describe a natural equivalence between three planar objects: weighted bipartite planar graphs; plana…
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…
Critical resonance in the non-intersecting lattice path model
Richard W. Kenyon, David B. Wilson
We study the phase transition in the honeycomb dimer model (equivalently, monotone non-intersecting lattice path model). At the critical point the system has a strong long-range de…