{
  "abstract": "We prove the existence of a sequence in $[0,1)$ with Poissonian pair correlation (PPC) and optimal-order star discrepancy $D_N^*=O((\\log N)/N)$, and further give a deterministic construction by applying a conditional-expectation rule to a nested dyadic random model. We also show that PPC imposes no universal discrepancy decay rate: for every positive sequence $ρ_N\\to0$, there exists a PPC sequence with $D_N^*/ρ_N\\to\\infty$. Under suitable regularity and growth assumptions, we realize prescribed discrepancy asymptotics, including $D_N^*\\sim c_βN^{-β}$ for every $0<β<1$, with $c_β>0$. We further construct a PPC sequence satisfying $D_N^*\\asymp(\\log N)/N$ for all sufficiently large $N$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06041",
  "author_total": 3,
  "authors": [
    {
      "name": "Bo Tan"
    },
    {
      "name": "Zhen Zhang"
    },
    {
      "name": "Qing-Long Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2122b7zeqpbbr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06041",
  "fulltext_url": null,
  "id": "2122b7zeqpbbr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06041",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "arxiv",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.06041",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2122b7zeqpbbr.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.06041",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06041"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Poissonian Pair Correlation and Discrepancy Rates",
  "title_text": "Poissonian Pair Correlation and Discrepancy Rates",
  "type": "preprint",
  "updated_at": "2026-11-08T21:20:29Z",
  "url": "https://research.draconitic.com/paper/2122b7zeqpbbr",
  "venue": "arXiv",
  "versions": []
}