Metraipolis › archive › dc_366a66887342

A Group Analogue of the Ghurye--Olkin--Ibragimov Theorem — arXiv:2609.19346

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.19346
License (as archived): CC0-1.0
Archived: 2026-10-10T04:23:35.180Z
SHA-256 of the archived text: fca41bda267e48e6f6620e600f1b540e75dc99eab069d2b52454d5f0a6a5b2cd
Stable URL of this page: https://metraipolis.com/documento/dc_366a66887342

How to cite

A Group Analogue of the Ghurye--Olkin--Ibragimov Theorem — arXiv:2609.19346 — arXiv (en), https://arxiv.org/abs/2609.19346 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_366a66887342 (Metraipolis archive dc_366a66887342, sha256 fca41bda267e48e6f6620e600f1b540e75dc99eab069d2b52454d5f0a6a5b2cd)

BibTeX

@misc{dc366a66887342,
  title = {A Group Analogue of the Ghurye--Olkin--Ibragimov Theorem — arXiv:2609.19346},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.19346},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_366a66887342; sha256 fca41bda267e48e6f6620e600f1b540e75dc99eab069d2b52454d5f0a6a5b2cd},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.19346. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

According to the classical Skitovich--Darmois theorem, the Gaussian distribution on the real line is characterized by the independence of two linear forms of a finite number of independent random variables $\xi_j$. This theorem has been extended in various directions. In particular, S.G. Ghurye and I. Olkin established an analogous result for the case where $\xi_j$ are $n$-dimensional independent random vectors and the coefficients of the linear forms are invertible $n\times n$ matrices. Subsequently, A.A. Zinger and later I.A. Ibragimov investigated linear forms of an infinite sequence of $n$-dimensional independent random vectors. In the present paper, we investigate, for the first time, linear forms of a sequence of independent random variables taking values in a second-countable locally compact Abelian group $X$ under either of the following conditions: $X$ contains no nontrivial compact subgroups, or $X$ contains no subgroups topologically isomorphic to the circle group and has a finite topological automorphism group. Furthermore, we investigate the case where the independent random variables take values in an $\mathbf{a}$-adic solenoid $\Sigma_{\mathbf{a}}$. In all these settings, the coefficients of the linear forms are topological automorphisms of the corresponding group.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-18 in math.PR).
Categorie arXiv: Probability (math.PR).
Pagina del lavoro: https://arxiv.org/abs/2609.19346 — 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 2026-10-10T04:09:58.336Z dalla pagina https://arxiv.org/catchup/math.PR/2026-09-18?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).