374 citations · 2.2k across the 47 of their papers we have counts for
30 papers · 1 filter
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…
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…
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…
Supercritical minimum mean-weight cycles
Jian Ding, Nike Sun, David B. Wilson
We study the weight and length of the minimum mean-weight cycle in the stochastic mean-field distance model, i.e., in the complete graph on vertices with edges weighted by inde…
Finitary Coloring
Alexander E. Holroyd, Oded Schramm, David B. Wilson
Suppose that the vertices of are assigned random colors via a finitary factor of independent identically distributed (iid) vertex-labels. That is, the color of vert…