Metraipolis › archive › dc_3e8a91ef7f7d

Wasserstein stability of the zero cell of a Poisson hyperplane tessellation under directional perturbations — arXiv:2608.13452

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.13452
License (as archived): CC0-1.0
Archived: 2026-10-19T04:47:25.790Z
SHA-256 of the archived text: a982fd2668957c78bec1a5a6f48ecfd22efa11e6c92aa967c372208bf6499e3a
Stable URL of this page: https://metraipolis.com/documento/dc_3e8a91ef7f7d

How to cite

Wasserstein stability of the zero cell of a Poisson hyperplane tessellation under directional perturbations — arXiv:2608.13452 — arXiv (en), https://arxiv.org/abs/2608.13452 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_3e8a91ef7f7d (Metraipolis archive dc_3e8a91ef7f7d, sha256 a982fd2668957c78bec1a5a6f48ecfd22efa11e6c92aa967c372208bf6499e3a)

BibTeX

@misc{dc3e8a91ef7f7d,
  title = {Wasserstein stability of the zero cell of a Poisson hyperplane tessellation under directional perturbations — arXiv:2608.13452},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.13452},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_3e8a91ef7f7d; sha256 a982fd2668957c78bec1a5a6f48ecfd22efa11e6c92aa967c372208bf6499e3a},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.13452. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

A stationary Poisson hyperplane process in $\mathbb{R}^d$ is characterized by an intensity parameter and an even probability measure on the unit sphere called the directional distribution. In this work, we investigate the stability of the zero cell, i.e., the random convex polytope of the induced hyperplane tessellation containing the origin, under perturbations of the directional distribution. Our results provide quantitative bounds establishing local Hölder continuity of the distribution of the zero cell with respect to Wasserstein metrics on the space of random convex bodies and probability distributions on the unit sphere. As an application, we establish stability bounds for density estimators constructed from Poisson hyperplane tessellations. In particular, we bound the expected total variation distance between the zero-cell-based estimated probability measures in terms of the Wasserstein distance between their directional distributions.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-08-14 in math.PR).
Categorie arXiv: Probability (math.PR).
Pagina del lavoro: https://arxiv.org/abs/2608.13452 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-19T04:27:45.060Z dalla pagina https://arxiv.org/catchup/math.PR/2026-08-14?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).