Related papers: Multiple-paths $SLE_\kappa$ in multiply connected …

Appreciation of Stochastic Loewner evolution (SLE$_\kappa$), as a powerful tool to check for conformal invariant properties of geometrical features of critical systems has been rising. In this paper we use this method to check conformal…

The Schramm-Loewner evolution (SLE_\kappa) is a candidate for the scaling limit of random curves arising in two-dimensional critical phenomena. When \kappa < 8, an instance of SLE_\kappa is a random planar curve with almost sure Hausdorff…

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 have conformal invariance properties in law. In the present…

We prove that the $SLE_\kappa$ trace in any simply connected domain $G$ is continuous (except possibly near its endpoints) if $\kappa<8$. We also prove an SLE analog of Makarov's Theorem about the support of harmonic measure.

We consider the Schramm-Loewner evolution (SLE$_\kappa$) for $\kappa \in (4,8)$, which is the regime that the curve is self-intersecting but not space-filling. We let ${\mathcal K}$ be the set of $\kappa \in (4,8)$ for which the adjacency…

We develop a theory of multiple radial SLE(0) -- a smooth system of curves in a simply connected domain $\Omega$ with marked boundary points $z_1, \ldots, z_n \in \partial \Omega$ and a marked interior point $q$ -- arising as the…

We construct a natural measure mu supported on the intersection of a chordal SLE(kappa) curve gamma with the real line R, in the range 4 < kappa < 8. The measure is a function of the SLE path in question. Assuming that boundary measures…

We aim at finding the reversal of radial SLE and proving the reversibility of whole-plane SLE. For this purpose, we define annulus SLE$(\kappa,\Lambda)$ processes in doubly connected domains with one marked boundary point. We derive some…

SLE(kappa; rho), a generalization of chordal Schramm-L\"owner evolution (SLE), is discussed from the point of view of statistical mechanics and conformal field theory (CFT). Certain ratios of CFT correlation functions are shown to be…

SLE(kappa,rho) is a generalisation of Schramm-Loewner evolution which describes planar curves which are statistically self-similar but not conformally invariant in the strict sense. We show that, in the context of boundary conformal field…

In the paper we prove that, for $\kappa\in(0,8)$, the $n$-point boundary Green's function of exponent $\frac8\kappa -1$ for chordal SLE$_\kappa$ exists. We also prove that the convergence is uniform over compact sets and the Green's…

Stochastic Loewner Evolutions (SLE) with a multiple sqrt(kappa)B of Brownian motion B as driving process are random planar curves (if kappa<=4) or growing compact sets generated by a curve (if kappa>4). We consider here more general Levy…

SLE is a random growth process based on Loewner's equation with driving parameter a one-dimensional Brownian motion running with speed $\kappa$. This process is intimately connected with scaling limits of percolation clusters and with the…

We give a new proof of the reversibility of the Schramm Loewner evolution for $\kappa \leq 4$. The main ideas used in the proof are similar to those used in the original proof of this result, given by Zhan.

We consider the Schramm-Loewner evolution (SLE$_\kappa$) for $\kappa \in (4,8)$, which is the regime where the curve is self-intersecting but not space-filling. We show that there exists $\delta_0>0$ such that for $\kappa \in (8 -…

We consider the Schramm-Loewner evolution (SLE$_\kappa$) with $\kappa=4$, the critical value of $\kappa > 0$ at or below which SLE$_\kappa$ is a simple curve and above which it is self-intersecting. We show that the range of an SLE$_4$…

We show that in the continuum limit watersheds dividing drainage basins are Schramm-Loewner Evolution (SLE) curves, being described by one single parameter $\kappa$. Several numerical evaluations are applied to ascertain this. All…

Schramm-Loewner Evolutions (SLEs) have proved an efficient way to describe a single continuous random conformally invariant interface in a simply-connected planar domain; the admissible probability distributions are parameterized by a…

Studying SLE$_{\kappa}$ on $S^2$ provides a new and interesting perspective for the conformality of some 2-dimensional physical models. We prove the existence and some basic properties of the spherical Minkowski content of SLE$_{\kappa}$,…

The present paper is concerned with properties of multiple Schramm--Loewner evolutions (SLEs) labelled by a parameter $\kappa\in (0,8]$. Specifically, we consider the solution of the multiple Loewner equation driven by a time change of…