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Schramm–Loewner Equations Driven by Symmetric Stable Processes

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Abstract

We consider shape, size and regularity of the hulls K t of the chordal Schramm–Loewner evolution driven by a symmetric α-stable process. We obtain derivative estimates, show that the domains \({\mathbb{H}{\setminus}K_{t}}\) are Hölder domains, prove that K t has Hausdorff dimension 1, and show that the trace is right-continuous with left limits almost surely.

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Authors and Affiliations

  1. Department of Mathematics, University of Washington, Seattle, WA, 98195, USA

    Zhen-Qing Chen & Steffen Rohde

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  1. Zhen-Qing Chen
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  2. Steffen Rohde
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Correspondence to Zhen-Qing Chen.

Additional information

Communicated by M. Aizenman

Research supported in part by NSF Grant DMS-0600206.

Research supported in part by NSF Grants DMS-0501726 and DMS-0244408.

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Chen, ZQ., Rohde, S. Schramm–Loewner Equations Driven by Symmetric Stable Processes. Commun. Math. Phys. 285, 799–824 (2009). https://doi.org/10.1007/s00220-008-0674-3

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  • DOI: https://doi.org/10.1007/s00220-008-0674-3

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