{
  "abstract": "Resampling is the standard remedy against weight degeneracy in particle filters, yet its effect on the spectrum of the particle second-moment matrix is poorly understood. We study a single resampling step for a d-dimensional ensemble of N particles with d/N -> c. For any unbiased scheme, the resampled empirical second-moment matrix dominates its pre-resampling counterpart in conditional convex order, while the conditional mean is preserved; the excess second spectral moment equals the Frobenius energy of the resampling perturbation. For multinomial resampling, the empirical count law converges to the mixed-Poisson law determined by the limiting weight law. For residual resampling, the count law is determined by the joint limit of floor-fraction pairs: we classify all residual limits of weight sequences converging to delta_1 in law as a one-parameter family between the deterministic identity and the full multinomial count law. Each count law feeds a common covariance-side spectral map, yielding exact consequences: a closed-form zero-eigenvalue mass, a rank-and-spectral-gap transition with a universal lower edge benchmark, computable regular edges, unbounded right support, and scheme-specific second-moment costs. The effective sample size determines one bulk statistic but cannot determine the limiting spectrum. Pre-registered numerical experiments confirm the theory at every level.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.16680",
  "author_total": 2,
  "authors": [
    {
      "name": "Deming Song"
    },
    {
      "name": "Chi Kin Lam"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/edhpbgh3be7gm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.16680",
  "fulltext_url": null,
  "id": "edhpbgh3be7gm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.16680",
  "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",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.16680",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/edhpbgh3be7gm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.16680",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.16680"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Spectral Costs of Multinomial and Residual Resampling in High-Dimensional Particle Ensembles: A Free-Probability Analysis",
  "title_text": "Spectral Costs of Multinomial and Residual Resampling in High-Dimensional Particle Ensembles: A Free-Probability Analysis",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:26Z",
  "url": "https://research.draconitic.com/paper/edhpbgh3be7gm",
  "venue": "arXiv",
  "versions": []
}