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

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 SLE_κ paths and then extend the recent work on Minkowski content to the intersection of an SLE path with the real line.