相关论文: Some Properties of Annulus SLE

For $\kappa\in(0,4]$, a family of annulus SLE$(\kappa;\Lambda)$ processes were introduced in [14] to prove the reversibility of whole-plane SLE$(\kappa)$. In this paper we prove that those annulus SLE$(\kappa;\Lambda)$ processes satisfy a…

We identify the local scaling limit of multiple boundary-to-boundary branches in a uniform spanning tree (UST) as a local multiple SLE(2), i.e., an SLE(2) process weighted by a suitable partition function. By recent results, this also…

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 aim at finding the reversal of radial SLE and proving the reversibility of whole-plane SLE. For this purpose, we define annulus SLE$(\kappa,\Lambda)$ processes in doubly connected domains with one marked boundary point. We derive some…

We improve the geometric properties of SLE$(\kappa;\vec{\rho})$ processes derived in an earlier paper, which are then used to obtain more results about the duality of SLE. We find that for $\kappa\in (4,8)$, the boundary of a standard…

We consider collections of $N$ chordal random curves obtained from a critical lattice model on a planar graph, in the limit when a fine-mesh graph approximates a simply-connected domain. We define and study candidates for such limits in…

Various features of the two-parameter family of Schramm-Loewner evolutions SLE(\kappa,\rho) are studied. In particular, we derive certain restriction properties that lead to a ``strong duality'' conjecture, which is an identity in law…

We derive some geometric properties of chordal SLE$(\kappa;\vec{\rho})$ processes. Using these results and the method of coupling two SLE processes, we prove that the outer boundary of the final hull of a chordal SLE$(\kappa;\vec{\rho})$…

A space of local martingales of SLE type growth processes forms a representation of Virasoro algebra, but apart from a few simplest cases not much is known about this representation. The purpose of this article is to exhibit examples of…

SLE is a random growth process based on Loewner's equation with driving parameter a one-dimensional Brownian motion running with speed $\kappa$. This process is intimately connected with scaling limits of percolation clusters and with the…

This paper introduces the annulus SLE$_\kappa$ processes in doubly connected domains. Annulus SLE$_6$ has the same law as stopped radial SLE$_6$, up to a time-change. For $\kappa\not=6$, some weak equivalence relation exists between annulus…

We establish anomalous inertial range scaling of structure functions for a model of advection of a passive scalar by a random velocity field. The velocity statistics is taken gaussian with decorrelation in time and velocity differences…

We consider multiple radial SLE curves with various time parameterizations and possible spiraling behavior. We construct them by tilting independent radial SLEs with a suitable local martingale, generalizing the earlier construction by…

We study SLE reversibility and duality using the Virasoro structure of the space of local martingales. For both problems we formulate a setup where the questions boil down to comparing two processes at a stopping time. We state algebraic…

We implement a version of conformal field theory in a doubly connected domain to connect it to the theory of annulus SLE of various types, including the standard annulus SLE, the reversible annulus SLE, and the annulus SLE with several…

We first prove that, for $\kappa\in(0,4)$, a whole-plane SLE$(\kappa;\kappa+2)$ trace stopped at a fixed capacity time satisfies reversibility. We then use this reversibility result to prove that, for $\kappa\in(0,4)$, a chordal…

Developing the theory of two-sided radial and chordal $\mathit{SLE}$, we prove that the natural parametrization on $\mathit{SLE}_{\kappa}$ curves is well defined for all $\kappa<8$. Our proof uses a two-interior-point local martingale.

The purpose of this note is to describe a framework which unifies radial, chordal and dipolar SLE. When the definition of SLE(kappa;rho) is extended to the setting where the force points can be in the interior of the domain, radial…

We derive boundary arm exponents and interior arm exponents for SLE$(\kappa)$. Combining with the possible convergence of critical lattice models to SLE, these exponents would give the corresponding alternating half-plane arm exponents and…

We derive boundary arm exponents for SLE. Combining with the convergence of critical lattice models to SLE, these exponents would give the alternating half-plane arm exponents for the corresponding lattice models.