11 citations · 13 across the 6 of their papers we have counts for
4 papers · 1 filter
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…
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…