Higher moments of the natural parameterization for SLE curves

Abstract

In this paper, we will show that the higher moments of the natural parametrization of SLE curves in any bounded domain in the upper half plane is finite. We prove this by estimating the probability that an SLE curve gets near n given points.

23 pages, 5 figures

References in corpus (2)

• Minkowski content and natural parameterization for the Schramm-Loewner evolution
• Multi-point Green's functions for SLE and an estimate of Beffara

Cited by in corpus (2)

• Uniqueness of the welding problem for SLE and Liouville quantum gravity
• Regularity of the Schramm-Loewner evolution: Up-to-constant variation and modulus of continuity