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Conformal restriction: The chordal case. (English) Zbl 1030.60096
In previous papers, the authors succeeded in computing the intersection exponents of SLE$$_6$$ (stochastic Loewner evolution). The determination of exponents for SLE$$_6$$ was also used to compute critical exponents for two-dimensional percolation. In the present paper, the authors go on investigating the chordal restriction measures and their relationship to SLE$$_k$$. They prove that there exists a one-parameter family P$$_{\alpha}$$ $$(\alpha\geq 5/8)$$ of such probability measures with P$$_{5/8}$$ being exactly the law of chordal SLE$$_{8/3}$$. A slightly different restriction property (right-sided property) is also studied; it is related to the reflected Brownian excursion and Bessel-type processes. These results help to understand the scaling limit and exponents of the two-dimensional self-avoiding walk and the relationship between SLE and conformal field theory.

##### MSC:
 60K35 Interacting random processes; statistical mechanics type models; percolation theory 82B27 Critical phenomena in equilibrium statistical mechanics 60J65 Brownian motion 30C99 Geometric function theory
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