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The covariant measure of SLE on the boundary
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  • Published: 10 November 2009

The covariant measure of SLE on the boundary

  • Tom Alberts1 &
  • Scott Sheffield2 

Probability Theory and Related Fields volume 149, pages 331–371 (2011)Cite this article

  • 121 Accesses

  • 11 Citations

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Abstract

We construct a natural measure μ supported on the intersection of a chordal SLE(κ) curve γ with \({\mathbb{R}}\) , in the range 4 < κ < 8. The measure is a function of the SLE path in question. Assuming that boundary measures transform in a “d-dimensional” way (where d is the Hausdorff dimension of \({\gamma \cap \mathbb{R}}\)), we show that the measure we construct is (up to multiplicative constant) the unique measure-valued function of the SLE path that satisfies the Domain Markov property.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Toronto, Toronto, ON, Canada

    Tom Alberts

  2. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, USA

    Scott Sheffield

Authors
  1. Tom Alberts
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  2. Scott Sheffield
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Corresponding author

Correspondence to Tom Alberts.

Additional information

T. Alberts’s research was supported in part by NSF Grant OISE 0730136. S. Sheffield’s research was supported in part by NSF Grants DMS 0403182, DMS 064558 and OISE 0730136.

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Alberts, T., Sheffield, S. The covariant measure of SLE on the boundary. Probab. Theory Relat. Fields 149, 331–371 (2011). https://doi.org/10.1007/s00440-009-0252-4

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  • Received: 17 November 2008

  • Published: 10 November 2009

  • Issue Date: April 2011

  • DOI: https://doi.org/10.1007/s00440-009-0252-4

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Mathematics Subject Classification (2000)

  • 60K35
  • 60D05
  • 82B21
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