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On conformally invariant CLE explorations. (English) Zbl 1290.60082
This paper gives two results about conformal loop ensembles (CLE) and Schramm-Loewner evolution (SLE), depending upon the values of their parameter. Firstly, it is shown that all the random-collections of SLE-type quasi-loops constructed via Sheffield’s asymmetric exploration trees have the same law. And the second result is related to the asymmetric explorations on the one hand, and the uniform exploration of CLE with index 4 on the other hand.

MSC:
60J67 Stochastic (Schramm-)Loewner evolution (SLE)
30C35 General theory of conformal mappings
30C80 Maximum principle, Schwarz’s lemma, Lindelöf principle, analogues and generalizations; subordination
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