{"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/another-marcenko-pastur-law-for-kendall-s-tau","title":"Another Marčenko-Pastur law for Kendall's tau","arxiv_id":"2503.18645","date":"2025-03-24","proceeding":null,"authors":["Pierre Bousseyroux","Tomas Espana","Matteo Smerlak"],"abstract":"Bandeira et al. (2017) show that the eigenvalues of the Kendall correlation matrix of $n$ i.i.d. random vectors in $\\mathbb{R}^p$ are asymptotically distributed like $1/3 + (2/3)Y_q$, where $Y_q$ has a Mar\\v{c}enko-Pastur law with parameter $q=\\lim(p/n)$ if $p, n\\to\\infty$ proportionately to one another. Here we show that another Mar\\v{c}enko-Pastur law emerges in the \"ultra-high dimensional\" scaling limit where $p\\sim q'\\, n^2/2$ for some $q'>0$: in this quadratic scaling regime, Kendall correlation eigenvalues converge weakly almost surely to $(1/3)Y_{q'}$.","url_abs":"https://arxiv.org/abs/2503.18645v2","url_pdf":"https://arxiv.org/pdf/2503.18645v2.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":"another-marcenko-pastur-law-for-kendall-s-tau","repo_url":"https://github.com/espanato/kendall_eigenvalues","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}