{
  "abstract": "For fixed $k\\ge3$, we determine the critical law of totally isotropic $r$-spaces for a uniform random map $Θ_N:Λ^k\\mathbb {F}_q^N\\to\\mathbb {F}_q^m$. At the exact balance $m\\binom rk=r(N-r)$, the entire null configuration is asymptotically an independent Bernoulli subset of $\\operatorname{Gr}(r,\\mathbb {F}_q^N)$ in total variation, uniformly in $q$ and $m$. Consequently, the counting measure $Ξ_r$ is asymptotically a Poisson point process, and its total mass $X_{N,r}$ is asymptotically Poisson. An exterior-rank stability theorem shows that near-extremal families decompose into Grassmann clusters with uniformly controlled span deficiency. We obtain quantitative rates and identify the first exterior-dependence scale. We also show that rare null $(r+1)$-spaces force high-order factorial-moment divergence, while the fixed-target bilinear cases $m=1,2$ exhibit non-Poisson critical behavior.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14340",
  "author_total": 1,
  "authors": [
    {
      "name": "Pakin Methawisal"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bnd42ta63b3sc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14340",
  "fulltext_url": null,
  "id": "bnd42ta63b3sc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14340",
  "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.CO"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7213286416",
  "pdf_url": "https://arxiv.org/pdf/2609.14340",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bnd42ta63b3sc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.14340",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14340"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Poisson laws and exterior stability for random alternating tensors",
  "title_text": "Poisson laws and exterior stability for random alternating tensors",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/bnd42ta63b3sc",
  "venue": "arXiv",
  "versions": []
}