{
  "abstract": "Motivated by applications in random geometry, we investigate the notion of subordination of snakes in the discrete setup. More precisely, given a random walk W indexed by a tree T and with steps in {..., -1, 0, 1}, we consider its subordinate tree obtained by contracting every edge of T that does not lead to a new record of the walk W. When the underlying tree T is a Bienaymé-Galton-Watson tree, we characterize the distribution of this subordinate tree. In particular, when T has a critical offspring distribution in an α-stable domain of attraction with α ∈ (1, 2], and under a light tails assumption on the steps, we prove that the associated subordinate tree is itself a Bienaymé-Galton-Watson tree with an offspring distribution in an α+1 2 -stable domain of attraction. Along the way, we obtain the asymptotic tail of the maximal displacement of the critical branching random walk W in this stable regime, under minimal assumptions. Finally, we use these results to prove scaling limit statements about the subordinate tree.\n\n1 Bienaymé trees are also known as Galton-Watson trees. See [1] for a quick discussion on those terminologies. 1",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02115",
  "author_total": 2,
  "authors": [
    {
      "name": "Antoine Aurillard"
    },
    {
      "name": "Mathieu Mourichoux"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6vaaxcaa4mn6g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02115",
  "fulltext_url": null,
  "id": "6vaaxcaa4mn6g",
  "issns": [],
  "landing_url": "https://hal.science/hal-05789911v1",
  "language": "en",
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
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      "hal",
      "0.math"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
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  "openalex": "W7216583493",
  "pdf_url": "https://hal.science/hal-05789911/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6vaaxcaa4mn6g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:53Z",
      "native_id": "hal-05789911",
      "source": "hal",
      "url": "https://hal.science/hal-05789911v1"
    },
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.02115",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02115"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Subordination of discrete snakes",
  "title_text": "Subordination of discrete snakes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/6vaaxcaa4mn6g",
  "venue": "HAL",
  "versions": []
}