We prove that the chordal contour lines of the discrete Gaussian free field converge to forms
of SLE (4). Specifically, there is a constant λ> 0 such that when h is an interpolation of the …

Abstract Fix constants χ> 0 χ> 0 and θ ∈ 0, 2 π) θ∈ 0, 2 π), and let h be an instance of the
Gaussian free field on a planar domain. We study flow lines of the vector field e^ i (h/χ+ θ) ei …

Percolation models describe the inside of a porous material. The theory emerged timidly in
the middle of the twentieth century before becoming one of the major objects of interest in …

The dimension of the SLE curves Page 1 The Annals of Probability 2008, Vol. 36, No. 4,
1421–1452 DOI: 10.1214/07-AOP364 © Institute of Mathematical Statistics, 2008 THE …

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 scaling …

Schramm-Loewner Evolutions (SLE) are random curves in planar simply connected
domains; the massless (Euclidean) free field in such a domain is a random distribution. Both …

We consider an embedding of planar maps into an equilateral triangle $\Delta $ which we
call the Cardy embedding. The embedding is a discrete approximation of a conformal map …

Suppose that D⊂ C is a Jordan domain and x, y ϵ∂ D are distinct. Fix k ϵ (4, 8), and let η
be an SLEk process from x to y in D. We prove that the law of the time-reversal of η is, up to …

Given a simply connected planar domain D, distinct points x,y∈∂D, and κ>0, the Schramm–
Loewner evolution SLE_κ is a random continuous non-self-crossing path in D from x to y …

What is the scaling limit of diffusion-limited aggregation (DLA) in the plane? This is an old
and famously difficult question. One can generalize the question in two ways: first, one may …