374 citations · 1.2k across the 68 of their papers we have counts for
5 papers · 2 filters
Gaussian free fields for mathematicians
Scott Sheffield
The d-dimensional Gaussian free field (GFF), also called the (Euclidean bosonic) massless free field, is a d-dimensional-time analog of Brownian motion. Just as Brownian motion is…
Linear speed large deviations for percolation clusters
Yevgeniy Kovchegov, Scott Sheffield
Let C_n be the origin-containing cluster in subcritical percolation on the lattice (1/n) Z^d, viewed as a random variable in the space Omega of compact, connected, origin-containin…
The harmonic explorer and its convergence to SLE(4)
Oded Schramm, Scott Sheffield
The harmonic explorer is a random grid path. Very roughly, at each step the harmonic explorer takes a turn to the right with probability equal to the discrete harmonic measure of t…
A large-deviation theorem for tree-indexed Markov chains
Amir Dembo, Peter Morters, Scott Sheffield
Given a finite typed rooted tree with vertices, the {\em empirical subtree measure} is the uniform measure on the typed subtrees of formed by taking all descendants…
Random Surfaces
Scott Sheffield
We study "random surfaces," which are random real (or integer) valued functions on Z^d. The laws are determined by convex, nearest neighbor, difference potentials that are invarian…