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Total Variation for the Lamplighter Walk on Z

For the switch-walk-switch walk on $\mathbb{Z}_2 \wr \mathbb{Z}$ started at $(0,0)$ and $(0,2)$, prove $\|P_t^x - P_t^y\|_{TV} \asymp t^{-1/2}$.

Exact FrontierDelta

Prior state unknownproved

Scope and record

Occurred: May 15, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: expert-verified. Publication: preprint. AI contribution: ai-discovered. Imported under CC BY 4.0.

Canonical aliases: Total Variation for the Lamplighter Walk on Z · Lamplighter TV

Confidence: Not scored

Registry verification: expert verified · preprint · resolved

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VibeMathed
registry · event recorded by

QED (GPT-5.5)
model · ai model contributor · OpenAI

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This event attributed to QED (GPT-5.5)

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