28 citations · 87 across the 8 of their papers we have counts for
7 papers · 1 filter
Limit shapes for the asymmetric five vertex model
Jan de Gier, Richard Kenyon, Samuel S. Watson
We compute the free energy and surface tension function for the five-vertex model, a model of non-intersecting monotone lattice paths on the grid in which each corner gets a positi…
Schnyder woods, SLE(16), and Liouville quantum gravity
Yiting Li, Xin Sun, Samuel S. Watson
In 1990, Schnyder used a 3-spanning-tree decomposition of a simple triangulation, now known as the Schnyder wood, to give a fundamental grid-embedding algorithm for planar maps. In…
Simple CLE in Doubly Connected Domains
Scott Sheffield, Samuel S. Watson, Hao Wu
We study Conformal Loop Ensemble (CLE) in doubly connected domains: annuli, the punctured disc, and the punctured plane. We restrict attention to CLE for which the loops ar…
Fractional Gaussian fields: a survey
Asad Lodhia, Scott Sheffield, Xin Sun +1
We discuss a family of random fields indexed by a parameter which we call the fractional Gaussian fields, given by \[ \mathrm{FGF}_s(\mathbb{R}^d)=(-Δ)^{-s/2} W,…
The conformal loop ensemble nesting field
Jason Miller, Samuel S. Watson, David B. Wilson
The conformal loop ensemble CLE with parameter is the canonical conformally invariant measure on countably infinite collections of non-crossing loops in a simply c…
Extreme nesting in the conformal loop ensemble
Jason Miller, Samuel S. Watson, David B. Wilson
The conformal loop ensemble with parameter is the canonical conformally invariant measure on countably infinite collections of noncrossing loops i…
Rate of Convergence for Cardy's Formula
Dana Mendelson, Asaf Nachmias, Samuel S. Watson
We show that crossing probabilities in 2D critical site percolation on the triangular lattice in a piecewise analytic Jordan domain converge with power law rate in the mesh size to…