A Baseline $T\log^2 T$ Upper Bound for KL-Regularized Prime--Zero Optimal Transport
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916942257848320 |
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| author | Yang, Zhejun |
| author_facet | Yang, Zhejun |
| contents | We prove that $\mathsf{OT}_η(T)\ll T\log^2 T$ unconditionally via a band-limited test scheme with Fejér averaging. The approach normalizes $\|\widehat f\|_1=Θ(T^{-1})$ to ensure $\|h\|_1\asymp T$ and $\|\widehat h\|_1\ll 1$, and applies an $L^1$-controlled smoothed explicit formula to bound the error terms. As a result, the prime--zero optimal transport distance admits the baseline $T\log^2 T$ upper bound without additional assumptions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_07329 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Baseline $T\log^2 T$ Upper Bound for KL-Regularized Prime--Zero Optimal Transport Yang, Zhejun Number Theory Classical Analysis and ODEs Probability 11M26 (Primary), 11M06 (Secondary) We prove that $\mathsf{OT}_η(T)\ll T\log^2 T$ unconditionally via a band-limited test scheme with Fejér averaging. The approach normalizes $\|\widehat f\|_1=Θ(T^{-1})$ to ensure $\|h\|_1\asymp T$ and $\|\widehat h\|_1\ll 1$, and applies an $L^1$-controlled smoothed explicit formula to bound the error terms. As a result, the prime--zero optimal transport distance admits the baseline $T\log^2 T$ upper bound without additional assumptions. |
| title | A Baseline $T\log^2 T$ Upper Bound for KL-Regularized Prime--Zero Optimal Transport |
| topic | Number Theory Classical Analysis and ODEs Probability 11M26 (Primary), 11M06 (Secondary) |
| url | https://arxiv.org/abs/2509.07329 |