Up-to-constants bounds on the two-point Green's function for SLE curves

TL;DR

This paper establishes up-to-constant bounds for the two-point Green's function of SLE curves, providing insights into the probability of the curves approaching two points.

Contribution

It provides the first up-to-constant bounds for the two-point Green's function of SLE, advancing understanding of SLE's probabilistic behavior.

Findings

Derived bounds for the two-point Green's function of SLE

Enhanced understanding of SLE curve proximity probabilities

Contributed to the mathematical theory of conformal invariance

Abstract

The Green's function for the chordal Schramm-Loewner evolution $SLE_\kappa$ for $0 < \kappa < 8$, gives the normalized probability of getting near points. We give up-to-constant bounds for the two-point Green's function.