OpenAI reports a positive finite Hausdorff gauge for SLE traces

For every fixed 0<κ<8, there is a deterministic Hausdorff gauge that almost surely gives positive finite measure to every nontrivial compact positive-time segment of ordinary chordal SLE_κ.

Curated contributions 1

Understand the problem ↓

Understanding the problem

Read the background

For every fixed 0<κ<8, there is a deterministic Hausdorff gauge that almost surely gives positive finite measure to every nontrivial compact positive-time segment of ordinary chordal SLE_κ.

Why it matters

If correct, answers Schramm’s Hausdorff-measure existence question for chordal SLE with 0<κ<8.

What counts as progress

Does a deterministic Hausdorff gauge assign positive finite measure to SLE trace segments?

Website timeline

Publication dates and editorial changes.