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bibkey: ouimet2020precise authors: Frédéric Ouimet year: 2020 title: A precise local limit theorem for the multinomial distribution and some applications doi: 10.1016/j.jspi.2021.03.006 url: https://arxiv.org/abs/2001.08512v4 claim: Theorem 2.1 and its proof supply classical local Gaussian estimates; PDF page 5, equations (3.6)-(3.7), gives the binomial power normalizations for powers two and three. strata_touched:

  • D5/S3/AnalyticClosure/BinomialLocalGaussian
  • D5/S3/AnalyticClosure/BinomialPowerNormalization
  • D5/S3/AnalyticClosure/BinomialUniformMaximum
  • D5/S3/AnalyticClosure/BinomialPoweredRatioMaximum license: citation-only triage: anchor

Classical local Gaussian estimates

The mathematical locator is arXiv:2001.08512v4, Theorem 2.1 and its proof, specialized to the binomial distribution. The local estimate controls the relative error on growing central windows. The repository uses the window |k-np|<=n^(7/12) for every fixed 0<p<1. It combines scalar Stirling and a logarithmic remainder bound in that specialization.

Equations (3.6)–(3.7) on PDF page 5 supply the complete binomial power normalizations for l=2 and l=3. They are not cited here as a statement covering every positive integer power. The arbitrary-power weighted complete-sum supplier is D5/L/Analytic/abel2013binomial, Theorem 3.1 for l>=2, with l=1 handled exactly.

Rendering note: the HTML rendering of arXiv:2001.08512v4 numbers these square/cube displays (3.12)–(3.13). In the v4 PDF, (3.12)–(3.13) on pages 6–7 concern the Bernstein tail bound and likelihood decomposition; the power-sum PDF locators are (3.6)–(3.7) on page 5.

The all-power tail and Gaussian lattice-sum statements in BinomialLocalGaussian and the uniform upper bound in BinomialUniformMaximum are repository formulations of classical analytic ingredients. The exact finite-sum formulations and their use in a truncated-ratio maximum are not attributed as verbatim statements of this source. No new discovery is claimed for the local Gaussian estimate.

The entropy expression used by BinomialLocalGaussian and BinomialMaximumLocalization is the already-frozen D5/S0/Diagonal/MarginBound.bernoulliKL, reused directly without a new definition or alias.

Verified locator

  • https://arxiv.org/abs/2001.08512v4
  • https://arxiv.org/pdf/2001.08512v4, Theorem 2.1 and proof, and page 5, equations (3.6)–(3.7).
  • https://arxiv.org/html/2001.08512v4, square/cube displays (3.12)–(3.13).
  • DOI: 10.1016/j.jspi.2021.03.006

The source-body findings are supplied by the bounded audit in #9357. The versioned abstract was consulted on 2026-09-21 UTC to verify author, title, DOI and version identity. The bibkey year is the original preprint year, 2020; v4 and the journal DOI date from 2021. The preprint locators do not assert inspection of the journal version’s numbering.