{
  "abstract": "Two-point correlation functions are a standard summary statistic in cosmic shear and large-scale-structure analyses. Their values are, however, constrained: non-negativity of the underlying power spectrum restricts any admissible sequence of correlation coefficients $(r_1,\\ldots,r_N)$ to a bounded convex region, described in the one-dimensional case by the recursive interval geometry of Schneider & Hartlap (2009). Their formalism introduces an affine variable $x_n$ that maps the admissible interval for $r_n$, given $r_1,\\ldots,r_{n-1}$, to $[-1,+1]$. We identify $x_n$ with the partial autocorrelation coefficient $α_n$ of the associated positive Toeplitz correlation matrix, a classical quantity in time-series analysis. The partial autocorrelations thus provide natural coordinates on the admissible region, each $α_n$ varying independently in $[-1,+1]$. This identification makes the standard partial-autocorrelation toolbox directly applicable. The admissible intervals for $r_n$, cumbersome to obtain at higher order in the original determinant-based formalism, now follow from an $\\mathcal{O}(N^2)$ recursion at arbitrary order. The inverse hyperbolic tangent used in the quasi-Gaussian likelihood construction of Wilking & Schneider (2013) becomes Fisher's $z$-transformation of partial autocorrelations, providing a classical statistical interpretation of its empirical Gaussianising effect. Numerical experiments illustrate the practical use of these natural coordinates in the tested one-dimensional settings. Higher-dimensional isotropic constraints require additional geometric input and lie outside the direct scope of this identification.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24500",
  "author_total": 1,
  "authors": [
    {
      "name": "Thomas Erben"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6vykjmfbt0q5y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24500",
  "fulltext_url": null,
  "id": "6vykjmfbt0q5y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24500",
  "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",
      "astro-ph.IM"
    ],
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      "arxiv",
      "math.MP"
    ],
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      "arxiv",
      "math.ST"
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      "arxiv",
      "stat.TH"
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      "openalex",
      "3103|Cosmology and Gravitation Theories"
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  ],
  "openalex": "W7214017284",
  "pdf_url": "https://arxiv.org/pdf/2609.24500",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6vykjmfbt0q5y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:19Z",
      "native_id": "2609.24500",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24500"
    }
  ],
  "subjects": [
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.IM",
      "subfield": "instrumentation-methods"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Natural coordinates for constrained correlation functions: Partial autocorrelations and the geometry of positive power spectra",
  "title_text": "Natural coordinates for constrained correlation functions: Partial autocorrelations and the geometry of positive power spectra",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:33Z",
  "url": "https://research.draconitic.com/paper/6vykjmfbt0q5y",
  "venue": "arXiv",
  "versions": []
}