相关论文: Fokker-Planck Equation of Schramm-Loewner Evolutio…
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…
The Shcramm-Loewner evolution (SLE) is a correlated exploration process, in which for the chordal set up, the tip of the trace evolves in a self-avoiding manner towards the infinity. The resulting curves are named SLE$_{\kappa}$,…
These notes survey the first results on large deviations of Schramm-Loewner evolutions (SLE) with emphasis on interrelations between rate functions and applications to complex analysis. More precisely, we describe the large deviations of…
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…
We derive the Ward identities of Conformal Field Theory (CFT) within the framework of Schramm-Loewner Evolution (SLE) and some related processes. This result, inspired by the observation that particular events of SLE have the correct…
Scharmm-Loewner evolution (SLE) and conformal field theory (CFT) are popular and widely used instruments to study critical behavior of two-dimensional models, but they use different objects. While SLE has natural connection with lattice…
We present a relation between conformal field theories (CFT) and radial stochastic Schramm-Loewner evolutions (SLE) similar to that we previously developed for the chordal SLEs. We construct an important local martingale using degenerate…
SLE(kappa; rho), a generalization of chordal Schramm-L\"owner evolution (SLE), is discussed from the point of view of statistical mechanics and conformal field theory (CFT). Certain ratios of CFT correlation functions are shown to be…
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…
Standard stochastic Loewner evolution (SLE) is driven by a continuous Brownian motion, which then produces a continuous fractal trace. If jumps are added to the driving function, the trace branches. We consider a generalized SLE driven by a…
Standard Schramm-Loewner evolution (SLE) is driven by a continuous Brownian motion which then produces a trace, a continuous fractal curve connecting the singular points of the motion. If jumps are added to the driving function, the trace…
Schramm-Loewner evolution appears as the scaling limit of interfaces in lattice models at critical point. Critical behavior of these models can be described by minimal models of conformal field theory. Certain CFT correlation functions are…
We apply the method of correlation functions to the coefficient problem in stochastic geometry. In particular, we give a proof for some universal patterns conjectured by M. Zinsmeister for the second moments of the Taylor coefficients for…
In previous work [AHP24], we proved a finite-time large deviation principle in the Hausdorff metric for multiradial Schramm-Loewner evolution, SLE$(\kappa)$, as $\kappa \to 0$, with good rate function being the multiradial Loewner energy.…
The aim of these notes is threefold. First, we discuss geometrical aspects of conformal covariance in stochastic Schramm-Loewner evolutions (SLEs). This leads us to introduce new ``dipolar'' SLEs, besides the known chordal, radial or…
We numerically show that the statistical properties of the shortest path on critical percolation clusters are consistent with the ones predicted for Schramm-Loewner evolution (SLE) curves for $\kappa=1.04\pm0.02$. The shortest path results…
This article provides an introduction to Schramm(stochastic)-Loewner evolution (SLE) and to its connection with conformal field theory, from the point of view of its application to two-dimensional critical behaviour. The emphasis is on the…
This manuscript explores the connections between a class of stochastic processes called "Stochastic Loewner Evolution" (SLE) and conformal field theory (CFT). First some important results are recalled which we utilise in the sequel, in…
We consider the measure on multiple chordal Schramm-Loewner evolution ($SLE_\kappa$) curves. We establish a derivative estimate and use it to give a direct proof that the partition function is $C^2$ if $\kappa<4$.
We review some of the results that have been derived in the last years on conformal invariance, scaling limits and properties of some two-dimensional random curves. In particular, we describe the intuitive ideas that lead to the definition…