Defining SLE in multiply connected domains with the Brownian loop measure

Details Defining SLE in multiply connected domains with the Brownian loop measure Defining SLE in multiply connected domains with the Brownian loop measure

2011-08-22

arxiv.org/abs/1108.4364v1

Mathematics

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Scientific paper

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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