Defining SLE in multiply connected domains with the Brownian loop measure

Abstract

We define the Schramm-Loewner evolution (SLE) in multiply connected domains for kappa \leq 4 using the Brownian loop measure. We show that in the case of the annulus, this is the same measure obtained recently by Dapeng Zhan. We use the loop formulation to give a different derivation of the partial differential equation for the partition function for the annulus.

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Cited by in corpus (7)

• Restriction Properties of Annulus SLE
• Reversibility of Whole-Plane SLE
• On the smoothness of the partition function for multiple Schramm-Loewner evolutions
• Schramm's formula for multiple loop-erased random walks
• Stochastic Komatu-Loewner evolutions and SLEs
• Conformal field theory for annulus SLE: partition functions and martingale-observables
• SLE and Virasoro representations: localization