{
  "abstract": "In classical models of supercritical continuous-time branching random walks (BRWs) on a $d$-dimensional lattice, the dimension $d$ is typically assumed to be fixed. When comparing the exponential growth rate $λ_0$ of a particle population in a BRW with a single branching source across lattices of different dimensions, a question arises whether it is possible to construct a family of random walks on $d$-dimensional lattices such that the model for a $(d+1)$-dimensional lattice ``inherits'' the properties of the model for a $d$-dimensional lattice in a meaningful sense. To address this question, the paper introduces the concept of a ``random walk on nested lattices'' and investigates the effect of the dimension $d$ on particle population growth using the ``inheritance'' condition. For an arbitrary symmetric random walk, a limit theorem is proved on the representation of the positive eigenvalue of the evolution operator for the mean particle numbers in terms of the process parameters and the dimension $d$, as the branching source intensity $β\\to \\infty$. The theorem shows that the influence of dimension persists even for very strong branching.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27129",
  "author_total": 1,
  "authors": [
    {
      "name": "Elena Yarovaya"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/51xybm54w7c6b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27129",
  "fulltext_url": null,
  "id": "51xybm54w7c6b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27129",
  "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",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7223148142",
  "pdf_url": "https://arxiv.org/pdf/2610.27129",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/51xybm54w7c6b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.27129",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27129"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Supercritical Branching Random Walks on Nested Lattices",
  "title_text": "Supercritical Branching Random Walks on Nested Lattices",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/51xybm54w7c6b",
  "venue": "arXiv",
  "versions": []
}