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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
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