374 citations · 2.2k across the 47 of their papers we have counts for
50 papers
The Green's function on the double cover of the grid and application to the uniform spanning tree trunk
Richard W. Kenyon, David B. Wilson
We compute the Green's function on the double cover of , branched over a vertex or a face. We use this result to compute the local statistics of the "trunk" of the u…
The six-vertex model and Schramm-Loewner evolution
Richard Kenyon, Jason Miller, Scott Sheffield +1
Square ice is a statistical mechanics model for two-dimensional ice, widely believed to have a conformally invariant scaling limit. We associate a Peano (space filling) curve to a…
Active spanning trees with bending energy on planar maps and SLE-decorated Liouville quantum gravity for
Ewain Gwynne, Adrien Kassel, Jason Miller +1
We introduce a two-parameter family of probability measures on spanning trees of a planar map. One of the parameters controls the activity of the spanning tree and the other is a m…
Active spanning trees and Schramm-Loewner evolution
Adrien Kassel, David B. Wilson
We consider the Peano curve separating a spanning tree from its dual spanning tree on an embedded planar graph, where the tree and dual tree are weighted by to the number of ac…
Bipolar orientations on planar maps and SLE
Richard Kenyon, Jason Miller, Scott Sheffield +1
We give bijections between bipolar-oriented (acyclic with unique source and sink) planar maps and certain random walks, which show that the uniformly random bipolar-oriented planar…
Sandpiles and unicycles on random planar maps
Xin Sun, David B. Wilson
We consider the abelian sandpile model and the uniform spanning unicycle on random planar maps. We show that the sandpile density converges to 5/2 as the maps get large. For the sp…