{
  "abstract": "We prove two families of distinguished cases of the heat flow conjecture for random matrices of Hall-Ho: elliptic Gaussian sources with planar targets, and deterministic Hermitian sources with targets on the boundary of the covariance disk. In particular, the empirical zero measure of the heat-evolved characteristic polynomial of a complex Ginibre matrix converges almost surely to the semicircle law. The strategy of the proof is to transfer estimates for the corresponding well-understood Gaussian matrix ensembles, through exact heat identities, into control of the zeros of the heat-evolved characteristic polynomials.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.05185",
  "author_total": 1,
  "authors": [
    {
      "name": "Theodoros Assiotis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4bva12qdkb0k7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.05185",
  "fulltext_url": null,
  "id": "4bva12qdkb0k7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.05185",
  "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-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2613|Random Matrices and Applications"
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  "openalex": "W7201881859",
  "pdf_url": "https://arxiv.org/pdf/2608.05185",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4bva12qdkb0k7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:19Z",
      "native_id": "2608.05185",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.05185"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "On the heat flow conjecture for random matrices",
  "title_text": "On the heat flow conjecture for random matrices",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/4bva12qdkb0k7",
  "venue": "arXiv",
  "versions": []
}