{
  "abstract": "We characterize the cases in which the minimal eigenvalues of interchange-process Laplacians on two Specht modules can be compared up to a positive multiplicative constant, independent of the edge rates. In the comparable cases, we establish an inverse-polynomial lower bound for this constant. We conjecture that the constant can always be taken to be 2/3. We apply these ideas to the mixing times of the interchange and exclusion processes. Using the comparison method of Hermon, Kozma and Salez, we prove that our conjecture implies a conjecture of Oliveira on the mixing time of the interchange process. We also obtain unconditional mixing-time bounds for both processes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.22151",
  "author_total": 1,
  "authors": [
    {
      "name": "Gil Alon"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/99g56e7k4prma.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.22151",
  "fulltext_url": null,
  "id": "99g56e7k4prma",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.22151",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7222615415",
  "pdf_url": "https://arxiv.org/pdf/2610.22151",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/99g56e7k4prma.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.22151",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.22151"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Spectral comparison on Specht modules and mixing of the interchange process",
  "title_text": "Spectral comparison on Specht modules and mixing of the interchange process",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/99g56e7k4prma",
  "venue": "arXiv",
  "versions": []
}