Restriction Properties of Annulus SLE

Details Restriction Properties of Annulus SLE Restriction Properties of Annulus SLE

2011-09-11

arxiv.org/abs/1109.2328v1

Mathematics

Probability

37 pages

Scientific paper

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.

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