{
  "abstract": "Rapid algorithmic developments have accelerated the sampling of redistricting ensembles (balanced graph partitions), yet evaluating rare events and sampling complex target measures remains a core challenge due to the high-dimensional and combinatorial nature of the phase space. We address a prerequisite for stratified sampling on this space: constructing and diagnosing candidate strata with suitable coverage and overlap. We build a grammar on observed plans by clustering districts into representative ``letters'' and using them to form plan-level ``words.'' A partition of unity over these words gives a soft assignment of plans to strata and allows us to estimate stratum masses and an overlap-induced flux matrix. We demonstrate this computational pipeline using real-world congressional redistricting data from Connecticut and examine how strata learned from one target distribution behave under related distributions. The resulting construction provides a foundation for future stratified sampling on spaces of redistricting plans or balanced graph partitions. We do not implement a complete stratified sampler here; evaluating whether the proposed strata improve sampling efficiency or reduce estimator variance is left for future work.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18741",
  "author_total": 5,
  "authors": [
    {
      "name": "Zijian Wang"
    },
    {
      "name": "Gregory J. Herschlag"
    },
    {
      "name": "Joon-Hyeok Yim"
    },
    {
      "name": "Jonathan C. Mattingly"
    },
    {
      "name": "Anna C. Gilbert"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7axe8x7fhqxm5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18741",
  "fulltext_url": null,
  "id": "7axe8x7fhqxm5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18741",
  "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.CY"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "arxiv",
      "physics.soc-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.18741",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7axe8x7fhqxm5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:01Z",
      "native_id": "2609.18741",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18741"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.soc-ph",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Towards stratified sampling for redistricting plans",
  "title_text": "Towards stratified sampling for redistricting plans",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/7axe8x7fhqxm5",
  "venue": "arXiv",
  "versions": []
}