{
  "abstract": "We study the high-dimensional asymptotics of Harish-Chandra-Itzykson-Zuber (HCIZ) integrals in the extensive-rank regime. The limit of these integrals is governed by a one-dimensional boundary-value hydrodynamical problem originally derived by Matytsin (1994) and rigorously proved by Guionnet and Zeitouni (2002). Despite its wide-ranging applications, explicit solutions to this problem are known only in a few specific cases. In this work, we introduce an efficient numerical scheme based on a particle discretization and prove its convergence to the continuous boundary-value problem for generic boundary densities. We validate our approach against known analytical solutions and apply it to generic densities, uncovering interesting dynamical phenomena. The high-dimensional limit of HCIZ integrals appears in various contexts, from the large deviations of random matrix spectra to the limiting free energy of disordered systems, high-dimensional statistics, and machine learning. As such, our contribution opens the way towards the numerical exploration of a wide range of high-dimensional models that were previously intractable.",
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  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07771",
  "author_total": 2,
  "authors": [
    {
      "name": "Antoine Maillard"
    },
    {
      "name": "Jean-Christophe Mourrat"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5d4dqs2pay7nq.bib",
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  "doi": "10.48550/arxiv.2609.07771",
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  "published": "2026-09-07",
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    {
      "first_seen": "2026-10-30T12:17:44Z",
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      "native_id": "2609.07771",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07771"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
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    {
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      "origin": "arxiv:cond-mat.dis-nn",
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  "title": "Efficient computation of the asymptotics of extensive-rank HCIZ integrals",
  "title_text": "Efficient computation of the asymptotics of extensive-rank HCIZ integrals",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/5d4dqs2pay7nq",
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