374 citations · 1.2k across the 68 of their papers we have counts for
7 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…
Dimers and Amoebae
Richard Kenyon, Andrei Okounkov, Scott Sheffield
We study random surfaces which arise as height functions of random perfect matchings (a.k.a. dimer configurations) on an weighted, bipartite, doubly periodic graph G embedded in th…
Dimers, Tilings and Trees
Richard Kenyon, Scott Sheffield
Generalizing results of Temperley, Brooks, Smith, Stone and Tutte and others we describe a natural equivalence between three planar objects: weighted bipartite planar graphs; plana…
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…