Abstract.
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, 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.
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Zhan, D. Stochastic Loewner evolution in doubly connected domains. Probab. Theory Relat. Fields 129, 340–380 (2004). https://doi.org/10.1007/s00440-004-0343-1
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DOI: https://doi.org/10.1007/s00440-004-0343-1