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