{
  "abstract": "For $\\beta \\in \\R$, we define the partition function $$ Z_\\beta(X) = \\sum_{i=1}^N \\exp(\\beta X_i) $$ of a centered Gaussian random vector $X=(X_1, \\ldots, X_N)$ with $\\E[X_i^2]= 1$. For $q \\in \\R$, we prove a complete phase transition for the generalized $L_q$-means of $Z_\\beta(X)$ at $q=1$. The centered Gaussian vector with covariance matrix $\\Delta_N$ obtained from a regular simplex configuration of unit vectors maximizes these means for $q<1$, and minimizes them for $q>1$. The two regimes are governed by different principles. For $q > 1$ {and $\\beta\\ne0$}, the moment functional is globally strongly convex on the entire set of correlation matrices, with an explicit modulus of convexity and a quantitative centroid-shape stability estimate. For $q<1$, the strategy is different. We prove a universal comparison for log-concave {profiles of reverse Brascamp--Lieb type.} Specializing {this result} to {the} Gumbel profile yields {a Laplace-transform} comparison between the partition functions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.38904",
  "author_total": 3,
  "authors": [
    {
      "name": "Omer Friedland"
    },
    {
      "name": "Olivier Guédon"
    },
    {
      "name": "Fabien Souli"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/750jk01azcgmm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.38904",
  "fulltext_url": null,
  "id": "750jk01azcgmm",
  "issns": [],
  "landing_url": "https://hal.science/hal-05764076v1",
  "language": "en",
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-fa"
    ],
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      "hal",
      "1.math.math-pr"
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    [
      "hal",
      "1.math.math-st"
    ],
    [
      "openalex",
      "2604|Mathematical Inequalities and Applications"
    ]
  ],
  "openalex": "W7214689228",
  "pdf_url": "https://hal.science/hal-05764076/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/750jk01azcgmm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:41Z",
      "native_id": "hal-05764076",
      "source": "hal",
      "url": "https://hal.science/hal-05764076v1"
    },
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.38904",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.38904"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "On partition functions of Gaussian random variables",
  "title_text": "On partition functions of Gaussian random variables",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:58Z",
  "url": "https://research.draconitic.com/paper/750jk01azcgmm",
  "venue": "HAL",
  "versions": []
}