Stationarity of SLE

TL;DR

This paper introduces a novel method to analyze the stationarity of SLE traces by examining the invariance of the conformal map law under an induced flow, applicable to the full SLE trace.

Contribution

It presents a new approach to study SLE hulls using conformal map invariance, enabling analysis of the entire SLE trace.

Findings

The law of the conformal map is invariant under a specific flow.

The method applies to SLE(kappa,rho) and the full SLE(kappa) trace.

Example calculations demonstrate the approach's effectiveness.

Abstract

A new method to study a stopped hull of SLE(kappa,rho) is presented. In this approach, the law of the conformal map associated to the hull is invariant under a SLE induced flow. The full trace of a chordal SLE(kappa) can be studied using this approach. Some example calculations are presented.