通过最优传输图实现前推操作的定量稳定性

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS ACS Applied Bio Materials Pub Date : 2024-07-19 DOI:10.1007/s10208-024-09669-4

Guillaume Carlier, Alex Delalande, Quentin Mérigot

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引用次数: 0

摘要

我们研究了用固定的（非光滑的）最优传输映射来关联一个度量的前推度量的映射的定量稳定性。在极少假设条件下，我们展示了这一操作的严密荷尔德行为。我们的证明主要依赖于一个新的约束，它量化了有界域上凸函数和利普希兹连续函数奇异集的大小。

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Quantitative Stability of the Pushforward Operation by an Optimal Transport Map

We study the quantitative stability of the mapping that to a measure associates its pushforward measure by a fixed (non-smooth) optimal transport map. We exhibit a tight Hölder-behavior for this operation under minimal assumptions. Our proof essentially relies on a new bound that quantifies the size of the singular sets of a convex and Lipschitz continuous function on a bounded domain.

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来源期刊

ACS Applied Bio Materials Chemistry-Chemistry (all)

CiteScore

9.40

自引率

2.10%

发文量

464