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Are random random walks normal? — arXiv:2610.01658

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.01658
License (as archived): CC0-1.0
Archived: 2026-10-06T17:35:55.880Z
SHA-256 of the archived text: 63c6526550c00cc7d80b2b4be1ab8bdedf9f47c42567b3b9ed522fc5fb45b059
Stable URL of this page: https://metraipolis.com/documento/dc_c930b5abe3fc

How to cite

Are random random walks normal? — arXiv:2610.01658 — arXiv (en), https://arxiv.org/abs/2610.01658 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_c930b5abe3fc (Metraipolis archive dc_c930b5abe3fc, sha256 63c6526550c00cc7d80b2b4be1ab8bdedf9f47c42567b3b9ed522fc5fb45b059)

BibTeX

@misc{dcc930b5abe3fc,
  title = {Are random random walks normal? — arXiv:2610.01658},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.01658},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_c930b5abe3fc; sha256 63c6526550c00cc7d80b2b4be1ab8bdedf9f47c42567b3b9ed522fc5fb45b059},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.01658. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Given a symmetric simple random walk $(X_n)_{n \ge 0}$, the family of all symmetric simple random walks $(Y_n)_{n \ge 0}$ adapted to the filtration of $(X_n)_{n \ge 0}$ was studied in Collevecchio et al. (2022). In particular, the authors established necessary and sufficient conditions under which the suitably normalized two-dimensional process $((X_n, Y_n))_{n \ge 0}$ converges weakly to a two-dimensional Brownian motion. When this occurs, we say that the random walk $(Y_n)_n$ is normal (with respect to $(X_n)_n$). In this paper, we investigate whether a "randomly selected" $(Y_n)_{n \ge 0}$ is normal. We consider a very general randomization procedure and look at both the quenched and annealed settings.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-10-02 in math.PR).
Categorie arXiv: Probability (math.PR).
Pagina del lavoro: https://arxiv.org/abs/2610.01658 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-06T16:02:27.477Z dalla pagina https://arxiv.org/catchup/math.PR/2026-10-02?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).