{"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/large-deviations-of-extreme-eigenvalues-of","title":"Large deviations of extreme eigenvalues of generalized sample covariance matrices","arxiv_id":"2008.09496","date":"2020-08-21","proceeding":null,"authors":["Antoine Maillard"],"abstract":"We present an analytical technique to compute the probability of rare events in which the largest eigenvalue of a random matrix is atypically large (i.e.\\ the right tail of its large deviations). The results also transfer to the left tail of the large deviations of the smallest eigenvalue. The technique improves upon past methods by not requiring the explicit law of the eigenvalues, and we apply it to a large class of random matrices that were previously out of reach. In particular, we solve an open problem related to the performance of principal components analysis on highly correlated data, and open the way towards analyzing the high-dimensional landscapes of complex inference models. We probe our results using an importance sampling approach, effectively simulating events with probability as small as $10^{-100}$.","url_abs":"https://arxiv.org/abs/2008.09496v2","url_pdf":"https://arxiv.org/pdf/2008.09496v2.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":"large-deviations-of-extreme-eigenvalues-of","repo_url":"https://github.com/AnMaillard/LD_lmax_sample_covariance","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"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}