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Stochastic Loewner evolution in doubly connected domains
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  • Published: 25 March 2004

Stochastic Loewner evolution in doubly connected domains

  • Dapeng Zhan1 

Probability Theory and Related Fields volume 129, pages 340–380 (2004)Cite this article

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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Authors and Affiliations

  1. Department of Mathematics, California Institute of Technology, Pasadena, Mail code: 253-37, CA 91125, USA

    Dapeng Zhan

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  1. Dapeng Zhan
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Correspondence to Dapeng Zhan.

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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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  • Received: 12 October 2003

  • Revised: 19 January 2004

  • Published: 25 March 2004

  • Issue Date: July 2004

  • DOI: https://doi.org/10.1007/s00440-004-0343-1

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Keywords

  • Random Walk
  • Equivalence Relation
  • Reversibility Property
  • Stochastic Loewner Evolution
  • Full Plane
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