SLE(κ,ρ) martingales and duality

Abstract

Various features of the two-parameter family of Schramm-Loewner evolutions SLE(κ,ρ) 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 SLE(κ) process for κ\ge 4 and a variant of the SLE(16/κ) process.

Published at http://dx.doi.org/10.1214/009117904000000793 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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• Values of Brownian intersection exponents III: Two-sided exponents
• Hausdorff dimensions for SLE_6
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