Related papers: Time-reversal of multiple-force-point chordal $\ma…

We define intermediate SLE$_\kappa(\underline\rho)$ and reversed intermediate SLE$_\kappa(\underline\rho)$ processes using Appell-Lauricella multiple hypergeometric functions, and use them to describe the time-reversal of…

Given a simply connected planar domain D, distinct points x,y \in \partial D, and \kappa >0, the Schramm-Loewner evolution SLE_\kappa is a random continuous non-self-crossing path in the closure of D from x to y. The…

We derive some geometric properties of chordal SLE$(\kappa;\vec{\rho})$ processes. Using these results and the method of coupling two SLE processes, we prove that the outer boundary of the final hull of a chordal SLE$(\kappa;\vec{\rho})$…

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 prove that, for $\kappa\le 4$, backward chordal SLE$_\kappa$ admits backward chordal SLE$_\kappa(-4,-4)$ decomposition for the capacity parametrization. This means that, for any bounded measurable subset $U\subset Q_4:={\mathbb…

Whole-plane SLE$_\kappa$ is a random fractal curve between two points on the Riemann sphere. Zhan established for $\kappa \leq 4$ that whole-plane SLE$_\kappa$ is reversible, meaning invariant in law under conformal automorphisms swapping…

We establish existence and uniqueness for Gaussian free field flow lines started at {\em interior} points of a planar domain. We interpret these as rays of a random geometry with imaginary curvature and describe the way distinct rays…

We prove that, for $\kappa\in(0,4)$ and $\rho\ge (\kappa-4)/2$, the chordal SLE$(\kappa;\rho)$ trace started from $(0;0^+)$ or $(0;0^-)$ satisfies the reversibility property. And we obtain the equation for the reversal of the chordal…

We first prove that, for $\kappa\in(0,4)$, a whole-plane SLE$(\kappa;\kappa+2)$ trace stopped at a fixed capacity time satisfies reversibility. We then use this reversibility result to prove that, for $\kappa\in(0,4)$, a chordal…

SLE$_{\kappa}(\rho)$ is a variant of SLE$_{\kappa}$ where $\rho$ characterizes the repulsion (if $\rho>0$) or attraction $(\rho<0)$ from the boundary. This paper examines the probabilities of SLE$_{\kappa}(\rho)$ to get close to the…

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…

The main result of this paper is that, for $\kappa\in(0,4]$, whole-plane SLE$_\kappa$ satisfies reversibility, which means that the time-reversal of a whole-plane SLE$_\kappa$ trace is still a whole-plane SLE$_\kappa$ trace. In addition, we…

For $\kappa\in(0,4]$, a family of annulus SLE$(\kappa;\Lambda)$ processes were introduced in [14] to prove the reversibility of whole-plane SLE$(\kappa)$. In this paper we prove that those annulus SLE$(\kappa;\Lambda)$ processes satisfy a…

We prove that the chordal SLE$_{\kappa}$ trace is reversible for $\kappa\in(0,4]$.

We improve the geometric properties of SLE$(\kappa;\vec{\rho})$ processes derived in an earlier paper, which are then used to obtain more results about the duality of SLE. We find that for $\kappa\in (4,8)$, the boundary of a standard…

We give a simplified and complete proof of the convergence of the chordal exploration process in critical FK-Ising percolation to chordal SLE$_\kappa( \kappa-6)$ with $\kappa=16/3$. Our proof follows the classical excursion-construction of…

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,…

We prove that the chordal SLE$_\kappa$ trace is reversible for $\kappa\in(0,4]$.

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…

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…