{
  "abstract": "We study the eigenvalues of the negative Dirichlet Laplacian $-Δ$ in domain $D_{ε,N}$ obtained by removing $N$ Euclidean balls of radius $ε$ from a bounded open set $D\\subseteq\\mathbb R^d$ ($d\\ge2$). It is known that, for the balls centered at points drawn independently from a distribution with probability density $ρ$ and for $N\\to\\infty$ and $ε\\downarrow0$ so that the aggregate Newtonian capacity of the removed balls tends to some $κ>0$, the eigenvalues of $-Δ$ in $D_{ε,N}$ homogenize to those of the Schrödinger operator $-Δ+κρ$ in $D$. Here we prove that, for the eigenvalues that are simple in the limit, a multivariate Central Limit Theorem holds in all $d\\ge2$ under centering by expected values. Unlike earlier work in $d=3$ by Figari, Orlandi and Teta and, independently, Ozawa from 1980s that was based on resolvent expansions, we rely on martingale representations and one-ball perturbation asymptotic controlled by methods of harmonic analysis.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18013",
  "author_total": 2,
  "authors": [
    {
      "name": "Marek Biskup"
    },
    {
      "name": "Ryoki Fukushima"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3ay6995htdchv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18013",
  "fulltext_url": null,
  "id": "3ay6995htdchv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18013",
  "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-ph"
    ],
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "arxiv",
      "math.SP"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7221768101",
  "pdf_url": "https://arxiv.org/pdf/2610.18013",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3ay6995htdchv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:11Z",
      "native_id": "2610.18013",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18013"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Eigenvalue fluctuations for the crushed ice problem",
  "title_text": "Eigenvalue fluctuations for the crushed ice problem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/3ay6995htdchv",
  "venue": "arXiv",
  "versions": []
}