{
  "abstract": "Given $m \\in \\mathbb{N}$ and a $p$-random subset $A \\subseteq \\mathbb{N}$, we asymptotically determine $\\log \\Pr(|\\mathbb{N} \\setminus (A + A)| \\ge m)$ for $p$ above the threshold for this property. As an application, we show that a uniformly at random chosen subset $A \\subseteq \\{1, \\ldots, n\\}$ of size $k$ such that $|A + A| \\le λk$, for $λ= o(k^{1/4} / \\log^{1/2} n)$, with high probability belongs to an arithmetic progression of length $λk / 2 + o(λk)$. Both proofs are based on a bespoke container argument, exploiting the additive robustness of the considered sets.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.29680",
  "author_total": 2,
  "authors": [
    {
      "name": "Rajko Nenadov"
    },
    {
      "name": "Lander Verlinde"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1j49ggp21t9tm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.29680",
  "fulltext_url": null,
  "id": "1j49ggp21t9tm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.29680",
  "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"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7162767400",
  "pdf_url": "https://arxiv.org/pdf/2605.29680",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1j49ggp21t9tm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2605.29680",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.29680"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The typical structure of sets with large sumset",
  "title_text": "The typical structure of sets with large sumset",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/1j49ggp21t9tm",
  "venue": "arXiv",
  "versions": []
}