A multifractal boundary spectrum for SLE κ ( ρ )


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Abstract

Abstract: We study SLEκ(ρ) curves, with κ and ρ chosen so that the curves hit the boundary. More precisely, we study the sets on which the curves collide with the boundary at a prescribed “angle” and determine the almost sure Hausdorff dimensions of these sets. This is done by studying the moments of the spatial derivatives of the conformal maps gt, by employing the Girsanov theorem and using imaginary geometry techniques to derive a correlation estimate.

Description

Funder: University of Cambridge

Keywords
Article, Primary 60J67, Secondary 60D05
Journal Title
Probability Theory and Related Fields
Conference Name
Journal ISSN
0178-8051
1432-2064
Volume Title
178
Publisher
Springer Berlin Heidelberg