{
  "abstract": "We study infinite-dimensional Dyson Brownian motions obtained as limits of finite systems without rescaling the actual stochastic dynamics. For $β=2$, we construct determinantal processes on an extended space of initial data and prove convergence of their finite-dimensional distributions under essentially optimal conditions. This extends the seminal results of Katori and Tanemura. The additional parameters record information at infinity and enter through an associated Laguerre-Pólya entire function. Moreover, for explicit classes of configurations, we establish convergence on path space and the Markov property. We prove rescaled long-time convergence, in finite-dimensional distributions, to the stationary extended $\\mathsf{Sine}$ process from arbitrary symmetric initial configurations with power-law counting exponent $q\\in(0,2)$. This extends the integer lattice relaxation result of Katori and Tanemura which was the only such result for explicit deterministic initial conditions. For $β\\geq1$, we prove convergence of finite particle systems from regular initial data to the unique strong solution of an infinite-dimensional stochastic differential equation in a certain rigid-path-regularity class. This extends seminal works of Tsai and Osada. We finally derive a stochastic partial differential equation of Burgers-type for the Stieltjes transform of the dynamics.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.26386",
  "author_total": 2,
  "authors": [
    {
      "name": "Theodoros Assiotis"
    },
    {
      "name": "Fengyi Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/egzwbyr5rarhz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.26386",
  "fulltext_url": null,
  "id": "egzwbyr5rarhz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.26386",
  "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.PR"
    ],
    [
      "openalex",
      "2613|Random Matrices and Applications"
    ]
  ],
  "openalex": "W7214093815",
  "pdf_url": "https://arxiv.org/pdf/2609.26386",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/egzwbyr5rarhz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.26386",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.26386"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Infinite-dimensional Dyson Brownian motion(s)",
  "title_text": "Infinite-dimensional Dyson Brownian motion(s)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/egzwbyr5rarhz",
  "venue": "arXiv",
  "versions": []
}