Related papers: Hadamard's formula and couplings of SLEs with free…
The level lines of the Gaussian free field are known to be related to SLE(4). It is shown how this relation allows to define chordal SLE(4) processes on doubly connected domains, describing traces that are anchored on one of the two…
We study the level lines of a Gaussian free field in a planar domain with general boundary data $F$. We show that the level lines exist as continuous curves under the assumption that $F$ is regulated (i.e., admits left and right limits at…
We point out a new simple way to couple the Gaussian Free Field (GFF) with free boundary conditions in a two-dimensional domain with the GFF with zero boundary conditions in the same domain: Starting from the latter, one just has to sample…
Consider an instance $h$ of the Gaussian free field on a simply connected planar domain with boundary conditions $-\lambda$ on one boundary arc and $\lambda$ on the complementary arc, where $\lambda$ is the special constant $\sqrt{\pi/8}$.…
We prove that the chordal contour lines of the discrete Gaussian free field converge to forms of SLE(4). Specifically, there is a constant lambda > 0 such that when h is an interpolation of the discrete Gaussian free field on a Jordan…
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…
In this article, we construct samples of SLE-like curves out of samples of CLE and Poisson point process of Brownian excursions. We show that the law of these curves depends continuously on the intensity measure of the Brownian excursions.…
Let $h$ be an instance of Gaussian Free Field in a planar domain. We study level lines of $h$ starting from boundary points. We show that the level lines are random continuous curves which are variants of SLE$_4$ path. We show that the…
One way to uniquely define Schramm-Loewner Evolution (SLE) in multiply connected domains is to use the restriction property. This gives an implicit definition of a $\sigma$-finite measure on curves; yet it is in general not clear how to…
Schramm--Loewner evolution (SLE) has been one of the central topics in the probabilistic study of two-dimensional critical systems. It is a random curve in two dimensions to which a cluster interface in a critical lattice system is…
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…
It is known that a backward Schramm--Loewner evolution (SLE) is coupled with a free boundary Gaussian free field (GFF) with boundary perturbation to give conformal welding of quantum surfaces. Motivated by a generalization of conformal…
We consider a coupling of the Gaussian free field with slit holomorphic stochastic flows, called ($\delta,\sigma$)-SLE, which contains known SLE processes (chordal, radial, and dipolar) as particular cases. In physical terms, we study a…
The Rohde--Schramm theorem states that Schramm--Loewner Evolution with parameter $\kappa$ (or SLE$_\kappa$ for short) exists as a random curve, almost surely, if $\kappa \neq 8$. Here we give a new and concise proof of the result, based on…
We prove that the singularity structure of all n-point distributions of a state of a generalised real free scalar field in curved spacetime can be estimated if the two-point distribution is of Hadamard form. In particular this applies to…
From conformal field theory on the Riemann sphere, we implement its boundary version in a simply-connected domain using the Schottky double construction. We consider the statistical fields generated by background charge modification of the…
We develop a version of dipolar conformal field theory in a simply connected domain with the Dirichlet-Neumann boundary condition and central charge one. We prove that all correlation functions of the fields in the OPE family of Gaussian…
We consider the coulomb gas model on the upper half plane with different boundary conditions, namely Drichlet, Neuman and mixed. We related this model to SLE($\kappa,\rho$) theories. We derive a set of conditions connecting the total charge…
In this paper, we provide a framework of estimates for describing 2D scaling limits by Schramm's SLE curves. In particular, we show that a weak estimate on the probability of an annulus crossing implies that a random curve arising from a…
We construct a coupling between a massive GFF and a random curve in which the curve can be interpreted as the level line of the field and has the law of massive SLE$_4$. This coupling is obtained by reweighting the law of the standard…