PreprintarXiv licencearXiv
The occupation time of a random walk generated by the uniform random permutation--a GPT-6 Astra proof
Abstract
This note provide a proof of Conjecture 2.5 in Fang et al. (J. Appl. Probab., 58(4):851--867, 2021), with the help of \texttt{GPT-6 Astra}. We show that the number of edges lying above zero of a random walk generated from the uniform permutation has the discrete arcsine law. The proof is short but hinges on an unexpected representation. We also make several comments on solving the problem using large language models.
Related
- Persistent occupation and critical marked sums on branching random walks
- The K-theory of uniform Roe algebras for coarse structures generated by finite-rank free abelian subgroups
- Random Permutation Matrices Form a Basis with High Probability
- Centered Permutation Prefixes for SGD with Random Reshuffling: Sharp Rates, Hölder Geometry, and Composite Proximal Extensions
- Random dynamical systems generated by rough differential equations driven by controlled rough paths
BibTeX
@misc{tang2026occupation,
title = {{The occupation time of a random walk generated by the uniform random permutation--a GPT-6 Astra proof}},
author = {Wenpin Tang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25102},
eprint = {2609.25102},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25102},
}
RIS
TY - UNPB
TI - The occupation time of a random walk generated by the uniform random permutation--a GPT-6 Astra proof
AU - Wenpin Tang
PY - 2026
DA - 2026/09/20
PB - arXiv
DO - 10.48550/arxiv.2609.25102
UR - https://arxiv.org/abs/2609.25102
AB - This note provide a proof of Conjecture 2.5 in Fang et al. (J. Appl. Probab., 58(4):851--867, 2021), with the help of \texttt{GPT-6 Astra}. We show that the number of edges lying above zero of a random walk generated from the uniform permutation has the discrete arcsine law. The proof is short but hinges on an unexpected representation. We also make several comments on solving the problem using large language models.
ER -