Author

Xiao-Zhen Wang

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Preprint Oct 2026

Quantitative stability of optimal transport via regularization

We prove quantitative stability estimates for quadratic optimal transport maps by regularizing a Brenier potential and estimating the error in the duality gap. The source has an $L^p$ density, $p>1$, relative to a probability measure with a BV density. When one target lies in a fixed ball, we obtain the $W_2$ H\"older...

Song-Bo Wang, Xiao-Zhen Wang · 0 citations

Preprint Oct 2026

Curvature bounds for the cost of coherence in conditional optimal transport

We study the gap between the integrated direction-wise kinetic minima and the minimum expected Dirichlet energy of a joint particle realization of a prescribed two-parameter family of conditional probability measures. Under regular coarea assumptions with compact connected fibres and a star-shaped parameter domain, we...

Xiao-Zhen Wang, Xiang Zhou, Zi-Han Zhang · 0 citations