Return Probability for the Lamplighter Walk on a Tree
For the switch-walk-switch lamplighter walk on $\mathbb{Z}_2 \wr T_d$, prove the sharp asymptotic $p_{2n}(e,e) = \rho_d^{2n} \exp[-(\pi^2 (\log(d-1))^2 + o(1)) \frac{n}{\log^2 n}]$ with $\rho_d = \frac{2\sqrt{d-1}}{d}$.
Exact FrontierDelta
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: Return Probability for the Lamplighter Walk on a Tree · Lamplighter return
Confidence: Not scored
Registry verification: expert verified · preprint · resolved
Attribution
VibeMathed
registry · event recorded by
QED (GPT-5.5 Pro)
model · ai model contributor · OpenAI
Lineage and corrections
This event attributed to QED (GPT-5.5 Pro)