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.


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