A Baseline Tlog² T Upper Bound for KL-Regularized Prime--Zero Optimal Transport

2025/09/09 by Yang, Zhejun
#11M06 (Secondary) #11M26 (Primary) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Number Theory (math.NT) #Probability (math.PR)

paper · doi:10.48550/arxiv.2509.07329

Abstract

We prove that OT_η(T)≪ Tlog² 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≪ 1, and applies an L¹-controlled smoothed explicit formula to bound the error terms. As a result, the prime--zero optimal transport distance admits the baseline Tlog² T upper bound without additional assumptions.

Citations

• Unbalanced optimal transport: Dynamic and Kantorovich formulations

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