Related papers: Some Properties of Annulus SLE

Spectral density in the pseudoscalar and vector channels is extracted from the SU(2) lattice quenched data. It is shown to consist of three sharp poles within the energy range accessible on the lattice.

We prove upper bounds for the probability that a radial SLE$_{\kappa}$ curve, $\kappa\in(0,8)$, comes within specified radii of $n$ different points in the unit disc. Using this estimate, we then prove a similar upper bound for a…

We consider the boundary WZW model on a half-plane with a cut growing according to the Schramm-Loewner stochastic evolution and the boundary fields inserted at the tip of the cut and at infinity. We study necessary and sufficient conditions…

We point out that the probability law of a single domain wall separating clusters in ADE lattice models in a simply connected domain is identical to that of corresponding chordal curves in the lattice O(n) and Q-state Potts models, for…

We show that, under mild assumptions on the limiting curve, a sequence of simple chordal planar curves converges uniformly whenever certain Loewner driving functions converge. We extend this result to random curves. The random version…

Many results in stochastic analysis and mathematical finance involve local martingales. However, specific examples of strict local martingales are rare and analytically often rather unhandy. We study local martingales that follow a given…

We show that the modulus of continuity of the SLE$_4$ uniformizing map is given by $(\log \delta^{-1})^{-1/3+o(1)}$ as $\delta \to 0$. As a consequence of our analysis, we show that the Jones-Smirnov condition for conformal removability…

In this supplementary note, we study the traces of multiple SLE(0) systems with two or more additional marked points. For general chordal configurations, the traces correspond to the real locus of real rational functions; in the radial…

The main goal of this article is to understand the trace properties of nonlocal minimal graphs in~$\R^3$, i.e. nonlocal minimal surfaces with a graphical structure. We establish that at any boundary points at which the trace from inside…

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

We study scaling properties and topological aspects of the 2--d O(3) non--linear $\sigma$--model on the lattice with the parametrized fixed point action recently proposed by P.~Hasenfratz and F.~Niedermayer. The behavior of the mass gap…

This paper is inspired by Richards' work on large gaps between sums of two squares [10]. It is shown in [10] that there exist arbitrarily large values of $\lambda$ and $\mu$, where $\mu \geq C \log \lambda$, such that intervals $[\lambda,…

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 scaling behavior of the closed trajectories of a moving particle generated by randomly placed rotators or mirrors on a square or triangular lattice is studied numerically. For most concentrations of the scatterers the trajectories close…

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

We derive exponential bounds on probabilities of large deviations for "light tail" martingales taking values in finite-dimensional normed spaces. Our primary emphasis is on the case where the bounds are dimension-independent or nearly so.…

Biggins [Uniform convergence of martingales in the branching random walk. {\em Ann. Probab.}, 20(1):137--151, 1992] proved local uniform convergence of additive martingales in $d$-dimensional supercritical branching random walks at complex…

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 prove refined (variation and H\"older-type) regularity statements for the SLE trace (under capacity parametrisation). More precisely, we show that the trace has finite $\psi$-variation for $\psi(x) = x^d(\log 1/x)^{-d-\varepsilon}$ and…