{
  "abstract": "Let Gamma be a convex-cocompact group of isometries of a CAT(-1) space X and let Y to X/Gamma be a Galois cover with a word-hyperbolic group of deck transformations. We show that, for almost every geodesic xi with respect to the Bowen-Margulis-Sullivan measure on the lift of X/Gamma, there exist m,sigma > 0 and a standard Brownian motion B(s) such that, for any lambda > 1/4, d(p(g(s,xi)), o) = ms + sigma B(s) + o(s^lambda), where g(s,xi) denotes the geodesic flow acting on the geodesics of Y and p the canonical projection to Y. The result is a consequence of an almost sure invariance principle for random walks on hyperbolic groups with dependent increments. Its proof makes use of a new Ruelle operator theorem for skew products and Martin boundary techniques for random walks with dependent increments.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18053",
  "author_total": 2,
  "authors": [
    {
      "name": "Gil José Astudillo Hernandez"
    },
    {
      "name": "Manuel Stadlbauer"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6m2y97tt7sc60.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18053",
  "fulltext_url": null,
  "id": "6m2y97tt7sc60",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18053",
  "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.DS"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7213529688",
  "pdf_url": "https://arxiv.org/pdf/2609.18053",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6m2y97tt7sc60.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.18053",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18053"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "On fluctuations of the drift in hyperbolic groups",
  "title_text": "On fluctuations of the drift in hyperbolic groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/6m2y97tt7sc60",
  "venue": "arXiv",
  "versions": []
}