Stochastic Loewner evolution in doubly connected domains

This paper introduces the annulus SLEκ processes in doubly connected domains. Annulus SLE6 has the same law as stopped radial SLE6, up to a time-change. For κ 6= 6, some weak equivalence relation exists between annulus SLEκ and radial SLEκ. Annulus SLE2 is the scaling limit of the corresponding loop-erased conditional random walk, which implies that a certain form of SLE2 satisfies the reversibility property. We also consider the disc SLEκ process defined as a limiting case of the annulus SLE’s. Disc SLE6 has the same law as stopped full plane SLE6, up to a time-change. Disc SLE2 is the scaling limit of loop-erased random walk, and is the reversal of radial SLE2.