Dimension and natural parametrization for SLE curves

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.

References in corpus (1)

• Monte Carlo comparisons of the self-avoiding walk and SLE as parameterized curves

Cited by in corpus (6)

• LERW as an example of off-critical SLEs
• The Length of an SLE - Monte Carlo Studies
• Exact sampling of self-avoiding paths via discrete Schramm-Loewner evolution
• A survey on dynamical percolation
• The growth exponent for planar loop-erased random walk
• Intersection probabilities for a chordal SLE path and a semicircle