{
  "abstract": "Weak perturbations of the same size can lead to terminal Wasserstein errors of different orders. For infinitely divisible laws smoothed by a Gaussian, we differentiate their distribution functions with respect to variance-weighted Lévy characteristics. This includes distributional directions caused by moving atoms. We obtain first- and second-order expansions that are uniform over Lipschitz test functions. When the first response is nonzero, Gaussian analyticity gives the signed second coefficient of the Wasserstein--1 distance. When the first response vanishes, a finite second displacement moment is enough to obtain a quadratic response. Its coefficient is strictly positive if the displacement dispersion is nonzero. For local balanced remeshing, the error is comparable to the grid-alignment variance. This gives sharp quadratic grid rates for compactly supported densities and nonaligned atomic sequences. We derive metric speed and length along admissible non-atomic curves, and use the response to build a linear program with a proved bound on how much its error exceeds the infimum over the allowed class and consistent quadrature. We also prove a sharp transition as smoothing vanishes and give a multivariate second-order expansion. The appendix gives state-dependent response formulas and further stability estimates.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.01411",
  "author_total": 1,
  "authors": [
    {
      "name": "Alexandre Autran"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d2bnmq6nhmhct.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.01411",
  "fulltext_url": null,
  "id": "d2bnmq6nhmhct",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.01411",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7216450597",
  "pdf_url": "https://arxiv.org/pdf/2610.01411",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d2bnmq6nhmhct.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.01411",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.01411"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Second-order Wasserstein response for Lévy laws",
  "title_text": "Second-order Wasserstein response for Lévy laws",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/d2bnmq6nhmhct",
  "venue": "arXiv",
  "versions": []
}