Mixing Time of Kac's Walk on the Rotation Group

Kac's walk on the rotation group, introduced by Hastings in 1970, is a central high-dimensional Markov chain in statistical physics and computational science. The paper proves it mixes in $n^2 \log n$ steps, the conjectured optimal rate, closing the gap left by a long line of successive improvements.

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Apr 26, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-co-developed. Imported under CC BY 4.0.

Canonical aliases: Mixing Time of Kac's Walk on the Rotation Group · Kac's walk on SO(n)

Confidence: Not scored

Registry verification: unreviewed · preprint · resolved

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Attribution

VibeMathed
registry · event recorded by

Natesh S. Pillai
human · human collaborator

Aaron Smith
human · human collaborator

GPT Pro 5.4
model · ai model contributor · OpenAI

Lineage and corrections

This event attributed to Aaron Smith

This event attributed to Natesh S. Pillai

This event attributed to GPT Pro 5.4

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