Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.21744 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911703480926208 |
|---|---|
| author | An, Chenyang Pan, Minghao |
| author_facet | An, Chenyang Pan, Minghao |
| contents | We derive the sharp return-probability asymptotic for the switch--walk--switch lamplighter walk with lamp group $\mathbb Z_2$ over the infinite $d$-regular tree: \[
p_{2n}(e,e)
=
ρ_d^{2n}
\exp\left[
-\left(π^2(\log(d-1))^2+o(1)\right)
\frac{n}{\log^2 n}
\right]. \] The proofs were generated by QED, a multi-agent system co-developed by the authors, without human intervention beyond the specification of the problem. This provides a test case for the ability of AI systems to produce rigorous mathematical proofs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_21744 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Return Probability for the Switch--Walk--Switch Lamplighter Walk on a Regular Tree An, Chenyang Pan, Minghao Probability We derive the sharp return-probability asymptotic for the switch--walk--switch lamplighter walk with lamp group $\mathbb Z_2$ over the infinite $d$-regular tree: \[ p_{2n}(e,e) = ρ_d^{2n} \exp\left[ -\left(π^2(\log(d-1))^2+o(1)\right) \frac{n}{\log^2 n} \right]. \] The proofs were generated by QED, a multi-agent system co-developed by the authors, without human intervention beyond the specification of the problem. This provides a test case for the ability of AI systems to produce rigorous mathematical proofs. |
| title | Return Probability for the Switch--Walk--Switch Lamplighter Walk on a Regular Tree |
| topic | Probability |
| url | https://arxiv.org/abs/2605.21744 |