Journal of the Mathematical Society of Japan

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

Gregory F. LAWLER

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Abstract

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.

Article information

Source
J. Math. Soc. Japan, Volume 67, Number 4 (2015), 1631-1669.

Dates
First available in Project Euclid: 27 October 2015

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1445951160

Digital Object Identifier
doi:10.2969/jmsj/06741631

Mathematical Reviews number (MathSciNet)
MR3417507

Zentralblatt MATH identifier
1362.60069

Subjects
Primary: 60J67: Stochastic (Schramm-)Loewner evolution (SLE)

Keywords
Schramm-Loewner evolution Hausdorff dimension Minkowski content

Citation

LAWLER, Gregory F. Minkowski content of the intersection of a Schramm-Loewner evolution (SLE) curve with the real line. J. Math. Soc. Japan 67 (2015), no. 4, 1631--1669. doi:10.2969/jmsj/06741631. https://projecteuclid.org/euclid.jmsj/1445951160


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