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Closed-Form Gaussian Mixture Representations of d-Dimensional Triangulated Domains — arXiv:2611.00922

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.00922
License (as archived): CC0-1.0
Archived: 2026-11-03T18:47:43.413Z
SHA-256 of the archived text: e88a074c4e2941e722702cb7675379f2b2d8c5d47ff59fc1740bcbecb5951a19
Stable URL of this page: https://metraipolis.com/documento/dc_3ef2ca61bf22

How to cite

Closed-Form Gaussian Mixture Representations of d-Dimensional Triangulated Domains — arXiv:2611.00922 — arXiv (en), https://arxiv.org/abs/2611.00922 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_3ef2ca61bf22 (Metraipolis archive dc_3ef2ca61bf22, sha256 e88a074c4e2941e722702cb7675379f2b2d8c5d47ff59fc1740bcbecb5951a19)

BibTeX

@misc{dc3ef2ca61bf22,
  title = {Closed-Form Gaussian Mixture Representations of d-Dimensional Triangulated Domains — arXiv:2611.00922},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.00922},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_3ef2ca61bf22; sha256 e88a074c4e2941e722702cb7675379f2b2d8c5d47ff59fc1740bcbecb5951a19},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.00922. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We derive a Gaussian Mixture (GM) representation of a full-dimensional subset of Euclidean space with finite volume from a finite simplicial triangulation in closed form. On each simplex, we replace the uniform probability density function (PDF) with a Gaussian PDF that minimizes the Kullback--Leibler (KL) divergence, arriving at the information projection onto the family of Gaussian PDFs. By exploiting affine isomorphisms between simplices, the joint convexity and bijection invariance properties of the KL divergence, identities for Dirichlet PDFs, and a partition-of-unity argument, we establish a dimension-dependent but geometry-independent sharp upper bound on the global KL divergence between the resulting GM PDF and the uniform PDF on the original domain. Numerical examples illustrate the construction and demonstrate its potential in practical applications.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.PR, nuovi lavori del giorno).
Categorie arXiv: Information Theory (cs.IT) ; Numerical Analysis (math.NA); Probability (math.PR).
Pagina del lavoro: https://arxiv.org/abs/2611.00922 — 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 2026-11-03T18:15:07.748Z dalla pagina https://arxiv.org/list/math.PR/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).