128 citations · 165 across the 5 of their papers we have counts for
4 papers · 1 filter
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…
The asymptotic determinant of the discrete Laplacian
Richard Kenyon
We compute the asymptotic determinant of the discrete Laplacian on a simply-connected rectilinear region in R^2. As an application of this result, we prove that the growth exponent…
Dominos and the Gaussian free field
R. Kenyon
We define a scaling limit of the height function on the domino tiling model (dimer model) on simply-connected regions in Z^2 and show that it is the ``massless free field'', a Gaus…