Related papers: Large deviations of Schramm-Loewner evolutions: A …

Formal Loewner evolution is connected to conformal field theory. In this letter we introduce an extension of Loewner evolution, which consists of two coupled equations and connect the martingales of these equations to the null vectors of…

We present basic properties of Dipolar SLEs, a new version of stochastic Loewner evolutions (SLE) in which the critical interfaces end randomly on an interval of the boundary of a planar domain. We present a general argument explaining why…

There is an essentially unique way to associate to any Riemann surface a measure on its simple loops, such that the collection of measures satisfy a strong conformal invariance property. Wendelin Werner constructed these random simple loops…

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…

Links between certain stochastic evolutions of conformal maps and conformal field theory have been studied in the realm of SLE and by utilizing singular vectors in highest-weight modules of the Virasoro algebra. It was recently found that…

Letting~$N=\left\{N(t), t\geq0\right\}$ be a standard Poisson process, Stroock~ \cite{Stroock-1981} constructed a family of continuous processes by $$\Theta_{\epsilon}(t)=\int_0^t\theta_{\epsilon}(r)dr, \ \ \ \ \ 0 \le t \le 1,$$ where…

We prove a large deviations principle for the probabilistic Schwarzian Field Theory at low temperatures. We demonstrate that the good rate function is equal to the action of the Schwarzian Field Theory, and we find its minimisers. In…

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…

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$_{\kappa}$,…

We study some features of the energy of a deterministic chordal Loewner chain, which is defined as the Dirichlet energy of its driving function. In particular, using an interpretation of this energy as a large deviation rate function for…

We continue the study of null-vector equations in relation with partition functions of (systems of) Schramm-Loewner Evolutions (SLEs) by considering the question of fusion. Starting from $n$ commuting SLEs seeded at distinct points, the…

This paper initiates the study of the conformal field theory of the SLE$_\kappa$ loop measure $\nu$ for $\kappa\in(0,4]$, the range where the loop is almost surely simple. First, we construct two commuting representations…

We prove the existence of the Green's function for radial SLE(k) for k<8. Unlike the chordal case where an explicit formula for the Green's function is known for all values of k<8, we give an explicit formula only for k=4. For other values…

The forward and reverse Kullback-Leibler (KL) divergences arise as limiting objectives in learning and inference yet induce markedly different inductive biases that cannot be explained at the level of expectations alone. In this work, we…

We prove the existence and nontriviality of the $d$-dimensional 4 Minkowski content for the Schramm-Loewner evolution ($\mathrm {SLE}_{\kappa}$) with $\kappa<8$ and $d=1+\frac{\kappa}{8}$. We show that this is a multiple of the natural…

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 $\mathbb R$.…

Stochastic Loewner evolution also called Schramm Loewner evolution (abbreviated, SLE) is a rigorous tool in mathematics and statistical physics for generating and studying scale invariant or fractal random curves in two dimensions. The…

We prove existence (and simpleness) of the trace for both forward and backward Loewner chains under fairly general conditions on semimartingale drivers. As an application, we show that stochastic Komatu-Loewner evolutions SKLE$_{\alpha,b}$…

We study the late time evolution of negatively curved Friedmann--Le\-ma\^{\i}tre--Robert\-son--Walker (FLRW) models with a perfect fluid matter source and a scalar field nonminimally coupled to matter. Since, under mild assumptions on the…

We prove the large deviation principle (LDP) for posterior distributions arising from subfamilies of full exponential families, allowing misspecification of the model. Moreover, motivated by the so-called inverse Sanov Theorem (see e.g.…