374 citations · 1.2k across the 68 of their papers we have counts for
7 papers · 2 filters
Conformal weldings of random surfaces: SLE and the quantum gravity zipper
Scott Sheffield
We construct a conformal welding of two Liouville quantum gravity random surfaces and show that the interface between them is a random fractal curve called the Schramm-Loewner evol…
Logarithmic fluctuations for internal DLA
David Jerison, Lionel Levine, Scott Sheffield
Let each of n particles starting at the origin in Z^2 perform simple random walk until reaching a site with no other particles. Lawler, Bramson, and Griffeath proved that the resul…
A contour line of the continuum Gaussian free field
Oded Schramm, Scott Sheffield
Consider an instance of the Gaussian free field on a simply connected planar domain with boundary conditions on one boundary arc and on the complementary arc, where $λ…
Conformal Loop Ensembles: The Markovian characterization and the loop-soup construction
Scott Sheffield, Wendelin Werner
For random collections of self-avoiding loops in two-dimensional domains, we define a simple and natural conformal restriction property that is conjecturally satisfied by the scali…
Conformal Loop Ensembles: Construction via Loop-soups
Scott Sheffield, Wendelin Werner
The two-dimensional Brownian loop-soup is a Poissonian random collection of loops in a planar domain with an intensity parameter c. When c is not greater than 1, we show that the o…
Strong path convergence from Loewner driving function convergence
Scott Sheffield, Nike Sun
We show that, under mild assumptions on the limiting curve, a sequence of simple chordal planar curves converges uniformly whenever certain Loewner driving functions converge. We e…