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$$\text{SLE}(\kappa,\rho)$$ martingales and duality. (English) Zbl 1096.60037
Summary: Various features of the two-parameter family of Schramm-Loewner evolutions
$$\text{SLE}(\kappa,\rho)$$ are studied. In particular, we derive certain restriction properties that lead to a ‘strong duality’ conjecture, which is an identity in law between the outer boundary of a variant of the $$\text{SLE}(\kappa)$$ process for $$\kappa\geq 4$$ and a variant of the $$\text{SLE}(16/\kappa)$$ process.

##### MSC:
 60K35 Interacting random processes; statistical mechanics type models; percolation theory 60G17 Sample path properties 82B27 Critical phenomena in equilibrium statistical mechanics
##### Keywords:
restriction property; path decompositions
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##### References:
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