{
  "abstract": "The symmetric Dyson exclusion process (SDEP) is an exclusion process on the lattice with a long-range logarithmic Coulomb-type interaction. It appears in several equivalent forms: as symmetric random walkers conditioned, in the Doob-transform sense, not to collide; as the maximal-activity limit of a conditioned SSEP; and as a ground-state transform of the spin-1/2 XX chain. In this work, we exploit this latter representation to obtain exact evolution formulas from deterministic initial configurations. The resulting determinantal kernel is expressed through a finite interpolation expression in terms of Lagrange polynomials, leading to explicit density evolution in finite and infinite lattices. For the melting of a densely packed block, we show that the full hierarchy of density moments is governed by a finite-dimensional polynomial algebra, and we identify Catalan numbers in the leading time coefficients. We also derive the Euler-scale density profile and the arctic curve separating frozen and liquid regions, and show that they coincide with conjectured hydrodynamic results obtained in a previous work.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "name": "Ali Zahra"
    },
    {
      "name": "Jerome Dubail"
    },
    {
      "name": "G M Schütz"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/37dzwr3fjmkvr.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "37dzwr3fjmkvr",
  "issns": [],
  "landing_url": "https://hal.science/hal-05768996v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "0.phys"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05768996/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/37dzwr3fjmkvr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:43Z",
      "native_id": "hal-05768996",
      "source": "hal",
      "url": "https://hal.science/hal-05768996v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:0.math",
      "subfield": "general"
    },
    {
      "field": "physics",
      "origin": "hal:0.phys",
      "subfield": "general"
    }
  ],
  "title": "Exact Results for the Symmetric Dyson Exclusion Process",
  "title_text": "Exact Results for the Symmetric Dyson Exclusion Process",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:43Z",
  "url": "https://research.draconitic.com/paper/37dzwr3fjmkvr",
  "venue": "HAL",
  "versions": []
}