21 citations · 34 across the 7 of their papers we have counts for
8 papers
The asymmetric five vertex model on a rectangle
Jan de Gier, Richard Kenyon, Michael Wheeler +1
We derive a determinantal expression for the inhomogeneous asymmetric five vertex model in a rectangular geometry with arbitrary boundary conditions at the bottom and top. Standard…
A quantum N-dimer model
Daniel C. Douglas, Richard Kenyon, Nicholas Ovenhouse +2
We study a quantum version of the -dimer model from statistical mechanics, based on the formalism from quantum topology developed by Reshetikhin and Turaev (the latter which, in…
The multinomial dimer model
Richard Kenyon, Catherine Wolfram
The dimer model is a classical statistical mechanics model which is exactly solvable in two dimensions, but about which little is known in higher dimensions. In analogy with large…
Webs and multiwebs for the symplectic group
Richard Kenyon, Haihan Wu
We define -multiwebs on planar graphs and discuss their relation with -webs. On a planar graph with a symplectic local system we define a matrix whose Pfaffian…
Eigenvalues of matrix products
Richard Kenyon, Nicholas Ovenhouse
We study pairs of matrices such that the eigenvalues of , of and of the product are specified in advance. We show that the space of such pair…
Higher-rank dimer models
Richard Kenyon, Nicholas Ovenhouse
Let be a bipartite planar graph with edges directed from black to white. For each vertex let be a positive integer. A multiweb in is a multigraph with multiplicit…
Dimers and cluster integrable systems
A. B. Goncharov, R. Kenyon
We show that the dimer model on a bipartite graph on a torus gives rise to a quantum integrable system of special type - a cluster integrable system. The phase space of the classic…
Limit shapes and the complex burgers equation
Richard Kenyon, Andrei Okounkov
In this paper we study surfaces in R^3 that arise as limit shapes in a class of random surface models arising from dimer models. The limit shapes are minimizers of a surface tensio…