{
  "abstract": "Given a symmetric simple random walk (Xn)n≥0, the family of all symmetric simple random walks (Yn)n≥0 adapted to the filtration of (Xn)n≥0 was studied in Collevecchio et al. (2022). In particular, the authors established necessary and sufficient conditions under which the suitably normalized two-dimensional process ((Xn, Yn))n≥0 converges weakly to a two-dimensional Brownian motion. When this occurs, we say that the random walk (Yn)n is normal (with respect to (Xn)n). In this paper, we investigate whether a “randomly selected” (Yn)n≥0 is normal. We consider a very general randomization procedure and look at both the quenched and annealed settings.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.01658",
  "author_total": 2,
  "authors": [
    {
      "name": "Kais Hamza"
    },
    {
      "name": "Laurent Tournier"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5x5amcv58gngv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.01658",
  "fulltext_url": null,
  "id": "5x5amcv58gngv",
  "issns": [],
  "landing_url": "https://hal.science/hal-05786003v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-pr"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7216469511",
  "pdf_url": "https://hal.science/hal-05786003/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5x5amcv58gngv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:50Z",
      "native_id": "hal-05786003",
      "source": "hal",
      "url": "https://hal.science/hal-05786003v1"
    },
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.01658",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.01658"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Are random random walks normal?",
  "title_text": "Are random random walks normal?",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/5x5amcv58gngv",
  "venue": "HAL",
  "versions": []
}