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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.00775 |
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Table of Contents:
- We study the perturbation of a measure $μ\in \mathscr{P}(\mathbb{R})$ consisting in superposing two copies of $μ$, each slightly shifted by a small distance $\pm h$. The difference between $μ$ and its perturbation is measured with a Wasserstein distance. For any $μ$, this distance is bounded from above by $h$. We show that measures for which this critical rate is achieved when $h$ goes to 0 are characterized as the ones giving most of their mass to some particular porous sets. This is used to identify which measures $μ$ on the real line have a 2-Wasserstein tangent cone equal to the set of directions inducing curves with maximal initial speed.