Minkowski content of the intersection of a Schramm-Loewner evolution (SLE) curve with the real line

The Schramm-Loewner evolution (SLE) is a probability measure on random fractal curves that arise as scaling limits of two-dimensional statistical physics systems. In this paper we survey some results about the Hausdorff dimension and Minkowski content of {\rm SLE}_\kappa paths and then extend the re...

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Bibliographic Details
Published in:Journal of the Mathematical Society of Japan 2015, Vol.67 (4), p.1631-1669
Main Author: LAWLER, Gregory F.
Format: Article
Language:English
Subjects:
60J67
Hausdorff dimension
Minkowski content
Schramm-Loewner evolution
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Summary:The Schramm-Loewner evolution (SLE) is a probability measure on random fractal curves that arise as scaling limits of two-dimensional statistical physics systems. In this paper we survey some results about the Hausdorff dimension and Minkowski content of {\rm SLE}_\kappa paths and then extend the recent work on Minkowski content to the intersection of an SLE path with the real line.
ISSN:0025-5645
1881-2333
DOI:10.2969/jmsj/06741631