Dimension transformation formula for conformal maps into the complement of an SLE curve

Abstract We prove a formula relating the Hausdorff dimension of a deterministic Borel subset of $${\mathbb {R}}$$R and the Hausdorff dimension of its image under a conformal map from the upper half-plane to a complementary connected component of an $$\hbox {SLE}_\kappa $$SLEκ curve for $$\kappa \no...

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Bibliographic Details
Main Authors: Gwynne, Ewain, Holden, Nina, Miller, Jason
Other Authors: Massachusetts Institute of Technology. Department of Mathematics
Format: Article
Language:English
Published: Springer Berlin Heidelberg 2021
Online Access:https://hdl.handle.net/1721.1/131627