Schramm-Loewner Equations Driven by Symmetric Stable Processes

TL;DR

This paper investigates the geometric properties of hulls generated by Schramm-Loewner evolution driven by symmetric stable processes, establishing regularity, dimension, and continuity characteristics.

Contribution

It provides new derivative estimates, proves the hulls are Hölder domains, and determines the Hausdorff dimension and path regularity for the driven SLE.

Findings

Hull complements are Hölder domains

Hulls have Hausdorff dimension 1

Trace is right-continuous with left limits

Abstract

We consider shape, size and regularity of the hulls of the chordal Schramm-Loewner evolution driven by a symmetric alpha-stable process. We obtain derivative estimates, show that the complements of the hulls are Hoelder domains, prove that the hulls have Hausdorff dimension 1, and show that the trace is right-continuous with left limits almost surely.