## From CLE($$\kappa$$) to SLE($$\kappa,\rho$$)’s.(English)Zbl 1338.60205

The main purpose of this paper is to obtain methods for constructing samples of Schramm-Loewner evolution (SLE) curves out of the sample of a conformal loop ensemble (CLE), by using additional Brownian paths. A chordal SLE in a simply connected domain $$D$$ is a random curve that is joining two prescribed boundary points of $$D$$. In this paper, CLE is a random family of loops that is defined in a simply connected domain $$D$$, which consist of simple loops. SLE curves indexed by $$k$$, where $$8/3<k\leq4$$, are random simple continuous curves that join $$a$$ to $$b$$ with Hausdorff dimension $$1+k/8$$. The authors show how to connect together the loops of a simple CLE in order to construct samples of chordal SLE indexed by $$k$$ processes and their SLE indexed by $$k$$ variants.

### MSC:

 60J67 Stochastic (Schramm-)Loewner evolution (SLE) 28A80 Fractals
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