{
  "abstract": "We characterize, up to universal constants, the total variation distance between finite products of arbitrary probability measures by a simple formula. A theorem of Latala reduces this expression to one scalar equation. As an application, we characterize the sample complexity of equal-prior binary hypothesis testing uniformly in the weak-detection regime, where squared Hellinger distance alone does not determine the answer, and also characterize the TV distance between multinomial distributions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21049",
  "author_total": 4,
  "authors": [
    {
      "name": "Ariel Avital"
    },
    {
      "name": "Aryeh Kontorovich"
    },
    {
      "name": "Roman Vershynin"
    },
    {
      "name": "Guangyi Zou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5srzbvdhr6f43.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21049",
  "fulltext_url": null,
  "id": "5srzbvdhr6f43",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21049",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2613|Probability and Statistical Research"
    ]
  ],
  "openalex": "W7213888139",
  "pdf_url": "https://arxiv.org/pdf/2609.21049",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5srzbvdhr6f43.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2609.21049",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21049"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Total Variation Distance between Product Distributions: an Analytic Proxy",
  "title_text": "Total Variation Distance between Product Distributions: an Analytic Proxy",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:12Z",
  "url": "https://research.draconitic.com/paper/5srzbvdhr6f43",
  "venue": "arXiv",
  "versions": []
}