344 citations · 1.3k across the 59 of their papers we have counts for
24 papers · 1 filter
Multideterminantal measures
Richard Kenyon
We define multideterminantal probability measures, a family of probability measures on where , generalizing determinantal measures (which correspond to…
Six-vertex model with rare corners and random restricted permutations
Vadim Gorin, Richard Kenyon
We study limit shapes in two equivalent models: the six-vertex model in the limit and the random Mallows permutation with restricted permutation matrix. We give the Euler-L…
Planar -webs and the boundary measurement matrix
Richard Kenyon, Haolin Shi
We compute connection probabilities for reduced -webs in the triple-dimer model on circular planar graphs using the boundary measurement matrix (reduced Kasteleyn matrix). As on…
Limit shapes from harmonicity: dominos and the five vertex model
Richard Kenyon, István Prause
We discuss how to construct limit shapes for the domino tiling model (square lattice dimer model) and -vertex model, in appropriate polygonal domains. Our methods are based on t…
The multinomial tiling model
Richard Kenyon, Cosmin Pohoata
Given a graph and collection of subgraphs (called tiles), we consider covering with copies of tiles in so that each vertex is covered with a predetermined…
The genus-zero five-vertex model
Richard Kenyon, István Prause
We study the free energy and limit shape problem for the five-vertex model with periodic "genus zero" weights. We derive the exact phase diagram, free energy and surface tension fo…