374 citations · 1.2k across the 68 of their papers we have counts for
5 papers · 1 filter
Conformal radii for conformal loop ensembles
Oded Schramm, Scott Sheffield, David B. Wilson
The conformal loop ensembles CLE(k), defined for k in [8/3, 8], are random collections of loops in a planar domain which are conjectured scaling limits of the O(n) loop models. We…
Exploration trees and conformal loop ensembles
Scott Sheffield
We construct and study the conformal loop ensembles CLE(kappa), defined for all kappa between 8/3 and 8, using branching variants of SLE(kappa) called exploration trees. The confor…
Tug of war with noise: a game theoretic view of the p-Laplacian
Yuval Peres, Scott Sheffield
Fix a bounded domain Omega in R^d, a continuous function F on the boundary of Omega, and constants epsilon>0, p>1, and q>1 with p^{-1} + q^{-1} = 1. For each x in Omega, let u^epsi…
Contour lines of the two-dimensional discrete Gaussian free field
Oded Schramm, Scott Sheffield
We prove that the chordal contour lines of the discrete Gaussian free field converge to forms of SLE(4). Specifically, there is a constant lambda > 0 such that when h is an interpo…
Tug-of-war and the infinity Laplacian
Yuval Peres, Oded Schramm, Scott Sheffield +1
We prove that every bounded Lipschitz function F on a subset Y of a length space X admits a tautest extension to X, i.e., a unique Lipschitz extension u for which Lip_U u = Lip_{bo…