Related papers: Quasi-Sure Stochastic Analysis through Aggregation…

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…

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…

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.

In this article, we give an explicit relationship of SLE partition functions with Coulomb gas formalism of conformal field theory. We first construct a family of SLE$(\kappa)$ partition functions as Coulomb gas integrals and derive their…

Suppose that $\eta$ is a whole-plane space-filling SLE$_\kappa$ for $\kappa \in (4,8)$ from $\infty$ to $\infty$ parameterized by Lebesgue measure and normalized so that $\eta(0) = 0$. For each $T > 0$ and $\kappa \in (4,8)$ we let…

The development of Schramm--Loewner evolution (SLE) as the scaling limits of discrete models from statistical physics makes direct simulation of SLE an important task. The most common method, suggested by Marshall and Rohde \cite{MR05}, is…

We show how to connect together the loops of a simple Conformal Loop Ensemble (CLE) in order to construct samples of chordal SLE(\kappa) processes and their SLE(\kappa,\rho) variants, and we discuss some consequences of this construction.

This paper is on developing stochastic analysis simultaneously under a general family of probability measures that are not dominated by a single probability measure. The interest in this question originates from the probabilistic…

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…

We give estimates for the probability that a chordal, radial or two-sided radial SLE$_\kappa$ curve retreats far from its terminal point after coming close to it, for $\kappa \leq 4$. The estimates are uniform over all initial segments of…

We define multichordal CLE$_\kappa$ for $\kappa \in (4,8)$ as the conditional law of the remainder of a partially explored CLE$_\kappa$. The strands of a multichordal CLE$_\kappa$ have a random link pattern, and their law conditionally on…

We use Minkowski content (i.e., natural parametrization) of SLE to construct several types of SLE$_\kappa$ loop measures for $\kappa\in(0,8)$. First, we construct rooted SLE$_\kappa$ loop measures in the Riemann sphere $\widehat{\mathbb…

Schramm-Loewner evolution (SLE$_\kappa$) is classically studied via Loewner evolution with half-plane capacity parametrization, driven by $\sqrt{\kappa}$ times Brownian motion. This yields a (half-plane) valued random field $\gamma = \gamma…

This paper introduces a novel quasi-likelihood extension of the generalised Kendall \(\tau_{a}\) estimator, together with an extension of the Kemeny metric and its associated covariance and correlation forms. The central contribution is to…

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…

The goal of the present paper is to explain, based on properties of the conformal loop ensembles CLE$_\kappa$ (both with simple and non-simple loops, i.e., for the whole range $\kappa \in (8/3, 8)$) how to derive the connection…

We study the adjacency graph of bubbles---i.e., complementary connected components---of an SLE$_{\kappa}$ curve for $\kappa \in (4,8)$, with two such bubbles considered to be adjacent if their boundaries intersect. We show that this…

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…

This article pertains to the classification of multiple Schramm-Loewner evolutions (SLE). We construct the pure partition functions of multiple SLE$(\kappa)$ with $\kappa \in (0,4]$ and relate them to certain extremal multiple SLE measures,…

It is well know that $SLE_\kappa$ curves exhibit a phase transition at $\kappa=4$. For $\kappa\le 4$ they are simple curves with probability one, for $\kappa>4$ they are not. The standard proof is based on the analysis of the Bessel SDE of…