{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/an-extension-of-krishnan-s-central-limit","title":"An extension of Krishnan's central limit theorem to the Brown-Thompson groups","arxiv_id":"2405.17275","date":"2024-05-27","proceeding":null,"authors":["Valeriano Aiello"],"abstract":"We extend a central limit theorem, recently established for the Thompson group $F=F_2$ by Krishnan, to the Brown-Thompson groups $F_p$, where $p$ is any integer greater than or equal to $2$. The non-commutative probability space considered is the group algebra $\\mathbb{C}[F_p]$, equipped with the canonical trace. The random variables in question are $a_n:= (x_n + x_n^{-1})/\\sqrt{2}$, where $\\{x_i\\}_{i\\geq 0}$ represents the standard family of infinite generators. Analogously to the case of $F=F_2$, it is established that the limit distribution of $s_n = (a_0 + \\ldots + a_{n-1})/\\sqrt{n}$ converges to the standard normal distribution. Furthermore, it is demonstrated that for a state corresponding to Jones's oriented subgroup $\\vec{F}$, such a central limit theorem does not hold.","url_abs":"https://arxiv.org/abs/2405.17275v2","url_pdf":"https://arxiv.org/pdf/2405.17275v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"an-extension-of-krishnan-s-central-limit","repo_url":"https://github.com/valerianoaiello/clt_thompson","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}