Restriction Properties of Annulus SLE

Abstract

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 restriction property, which is similar to that for chordal SLE$(\kappa )$. Using this property, we construct $n\ge 2$ curves crossing an annulus such that, when any $n-1$ curves are given, the last curve is a chordal SLE$(\kappa )$ trace.

37 pages

References in corpus (3)

• The scaling limits of planar LERW in finitely connected domains
• Defining SLE in multiply connected domains with the Brownian loop measure
• Reversibility of Whole-Plane SLE

Cited by in corpus (2)

• Conformal field theory for annulus SLE: partition functions and martingale-observables
• Stochastic Komatu-Loewner evolutions and SLEs