{
  "abstract": "We consider a random growing graph model with two \\emph{types}, or \\emph{communities}, that belongs to the class of preferential attachment models. Starting from an initial graph $G_0$ in which each node has a type, the graph $G_{n+1}$ is generated by addition of a new node, which attaches through an edge to a node $v$ of $G_n$. The probability of attaching to $v$ depends on the communities of both the new node and $v$, and is proportional to $\\operatorname{deg}_n(v)^γ$, where $γ\\in[0, 1]$. We establish a convergence result for the limiting proportion of vertices of each degree and in each community in a certain regime of the parameter $γ$. To this end, we first use stochastic approximation techniques to reduce the convergence problem to the study of a non-linear evolution equation. We then use a probabilistic coupling approach to investigate the long-time behavior of the unique solution to this evolution equation. We emphasize that the techniques previously used to handle the single-community case cannot be extended directly to our setting. Indeed, the associated continuous-time embedding is not a multitype branching process in the usual sense, since the transition rates at any given time $t$ depend on the entire graph structure at that time.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06904",
  "author_total": 3,
  "authors": [
    {
      "name": "Anna Ben-Hamou"
    },
    {
      "name": "Nicolas Broutin"
    },
    {
      "name": "Camille Cazaux"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2r9p2afwyb7q2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06904",
  "fulltext_url": null,
  "id": "2r9p2afwyb7q2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06904",
  "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",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.06904",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2r9p2afwyb7q2.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.06904",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06904"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Sublinear multi-type preferential attachment",
  "title_text": "Sublinear multi-type preferential attachment",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:31Z",
  "url": "https://research.draconitic.com/paper/2r9p2afwyb7q2",
  "venue": "arXiv",
  "versions": []
}