Higher moments of the natural parameterization for SLE curves
Mohammad A. Rezaei, Dapeng Zhan
TL;DR
This paper proves that the higher moments of the natural parametrization of SLE curves are finite by estimating the probability of the curve approaching multiple points.
Contribution
It introduces a method to establish finiteness of higher moments for SLE natural parametrization through probabilistic estimates.
Findings
Higher moments of SLE natural parametrization are finite.
Probabilistic estimates of SLE curves near multiple points are developed.
The results apply to SLE in any bounded domain in the upper half plane.
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.
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