Dimension and natural parametrization for SLE curves

2007/12/19 by Gregory F. Lawler, Lawler, Gregory F.
Mathematics · Physics and Astronomy · #60J15 #82B27 #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #Probability (math.PR) #Stochastic processes and statistical mechanics #math-ph #math.MP #math.PR #msc:60J15 #msc:82B27

paper · pdf · doi:10.48550/arxiv.0712.3263

arxiv created 2007/12/19 · openalex publication_date 2007/12/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Some possible definitions for the natural parametrization of SLE (Schramm-Loewner evolution) paths are proposed in terms of various limits. One of the definitions is used to give a new proof of the Hausdorff dimension of SLE paths.

Citations

• Monte Carlo comparisons of the self-avoiding walk and SLE as parameterized curves
• Fractal Geometry: Mathematical Foundations and Applications.

Related

• Intersections of SLE Paths: the double and cut point dimension of SLE
• Dimension transformation formula for conformal maps into the complement\n of an SLE curve
• Basic properties of the natural parametrization for the Schramm-Loewner evolution
• Hausdorff dimensions for SLE6
• Decomposition of Schramm-Loewner evolution along its curve