Related papers: Duality of Chordal SLE, II

Chordal SLE$_\kappa(\underline{\rho})$ is a natural variant of chordal SLE curve. It is a family of random non-crossing curves on the upper half plane from 0 to $\infty$, whose law is influenced by additional force points on $\mathbb R$.…

We consider chordal SLE(kappa) curves for kappa > 4, where the intersection of the curve with the boundary is a random fractal of almost sure Hausdorff dimension min {2-8/kappa,1}. We study the random sets of points at which the curve…

We derive a number of estimates for the probability that a chordal SLE path in the upper half plane H intersects a semicircle centred on the real line. We prove that if 0<kappa<8 and gamma:[0,infinity) to closure(H) is a chordal SLE in H…

We prove upper bounds for the probability that a radial SLE$_{\kappa}$ curve, $\kappa\in(0,8)$, comes within specified radii of $n$ different points in the unit disc. Using this estimate, we then prove a similar upper bound for a…

The purpose of this note is to describe a framework which unifies radial, chordal and dipolar SLE. When the definition of SLE(kappa;rho) is extended to the setting where the force points can be in the interior of the domain, radial…

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…

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 prove that for almost every Brownian motion sample, the corresponding SLE(\kappa) curves parameterized by capacity exist and change continuously in the supremum norm when \kappa varies in the interval [0,\kappa_0), where…

We show that, for $\kappa\in(0,8)$, the integral of the laws of two-sided radial SLE$_\kappa$ curves through different interior points against a measure with SLE$_\kappa$ Green function density is the law of a chordal SLE$_\kappa$ curve,…

SLE($\kappa,\rho$) is a variant of the Schramm-Loewner Evolution which describes the curves which are not conformal invariant, but are self-similar due to the presence of some other preferred points on the boundary. In this paper we study…

Questions regarding the continuity in $\kappa$ of the $SLE_{\kappa}$ traces and maps appear very naturally in the study of SLE. In order to study the first question, we consider a natural coupling of SLE traces: for different values of…

Suppose that D is a planar Jordan domain and x and y are distinct boundary points of D. Fix \kappa \in (4,8) and let \eta\ be an SLE_\kappa process from x to y in D. We prove that the law of the time-reversal of \eta is, up to…

We consider the boundary WZW model on a half-plane with a cut growing according to the Schramm-Loewner stochastic evolution and the boundary fields inserted at the tip of the cut and at infinity. We study necessary and sufficient conditions…

In this paper, we consider hypergeometric SLE process for $\kappa\in (4,8)$ and $\nu>\frac{\kappa}{2}-6$. Though the definition of hypergeometric SLE process is complicated, we show that given its hitting point on a specific boundary, its…

We prove the existence and uniqueness of multiple SLE$_\kappa$ associated with any given link pattern for $\kappa\in (4,6]$. We also have the uniqueness for $\kappa\in (6,8)$. The multiple SLE$_\kappa$ law is constructed by first…

This article employs Schramm-Loewner Evolution to obtain intersection exponents for several chordal $SLE_{8/3}$ curves in a wedge. As $SLE_{8/3}$ is believed to describe the continuum limit of self-avoiding walks, these exponents correspond…

The natural paramterization or length for the Schramm-Loewner evolution (SLE{\kappa}) is the candidate for the scaling limit of the length of discrete curves for \kappa < 8. We improve the proof of the existence of the parametrization and…

When studying stochastic processes, it is often fruitful to have an understanding of several different notions of regularity. One such notion is the optimal H\"older exponent obtainable under reparametrization. In this paper, we show that…

We establish an upper bound on the asymptotic probability of an SLE(kappa) curve hitting two small intervals on the real line as the interval width goes to zero, for the range 4 < kappa < 8. As a consequence we are able to prove that the…

An annulus SLE$_\kappa$ trace tends to a single point on the target circle, and the density function of the end point satisfies some differential equation. Some martingales or local martingales are found for annulus SLE$_4$, SLE$_8$ and…