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Conformal loop ensembles: the Markovian characterization and the loop-soup construction. (English) Zbl 1271.60090
We have at hand an algebra for curves endowed with certain selected properties. A chordal Schramm-Loewner evolution (SLE) is a random non-self-traversing curve in a simply connected domain, joining two prescribed boundary points of the domain; and a conformal loop ensemble (CLE) is a random collection of loops which combine conformal invariance with a natural restriction property suggested by the fact that the discrete analog of this property trivially holds for some discrete models. These CLE ensembles are constructed by two different ways: one is based on SLE and the other one is based on loop-soup.The main purpose of the paper is to show that, to some extent, there is a complete equivalence between SLE and CLE. All these results, which refer to Brownian motion, fractals, percolation, Poisson processes, find their use in the application of conformal field theory to physics.

##### MSC:
 60J67 Stochastic (Schramm-)Loewner evolution (SLE)
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