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≥ 4 and a variant of the SLE(16/κ) process. © Institute of Mathematical Statistics, 2005.