{
  "abstract": "We study the communication cost of exact sampling under Campbell's exponential coding criterion. Given a target distribution $P$ and a proposal distribution $Q$, the sender and receiver share i.i.d. $Q$-distributed samples, and the sender communicates an index so that the selected sample has distribution exactly $P$. We introduce a new information measure Rényi channel simulation divergence $R_α(P\\Vert Q)$, a Rényi generalization of the channel simulation divergence. We then show that it lower bounds the Campbell cost of every exact sampler and is achievable, via a new layered sampling scheme, within an additive constant depending only on the Campbell parameter. This yields a tighter one-shot characterization than previous bounds based on Rényi divergences of different orders. For i.i.d. product distributions, under suitable non-degeneracy and moment conditions, we further show that the gap beyond the leading Rényi-divergence term is $\\frac{1}{2}\\log n+O(1)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15656",
  "author_total": 2,
  "authors": [
    {
      "name": "Yijun Fan"
    },
    {
      "name": "Aaron B. Wagner"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f3t7c92ey72m4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15656",
  "fulltext_url": null,
  "id": "f3t7c92ey72m4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15656",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "2613|Markov Chains and Monte Carlo Methods"
    ]
  ],
  "openalex": "W7221786223",
  "pdf_url": "https://arxiv.org/pdf/2610.15656",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f3t7c92ey72m4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15656",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15656"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2613|Markov Chains and Monte Carlo Methods",
      "subfield": "statistics"
    }
  ],
  "title": "Exact Sampling Under Campbell Cost via Rényi Channel Simulation Divergence",
  "title_text": "Exact Sampling Under Campbell Cost via Rényi Channel Simulation Divergence",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/f3t7c92ey72m4",
  "venue": "arXiv",
  "versions": []
}