## 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

#### 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

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)

#### 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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