{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:17:40Z","timestamp":1760145460346,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2024,7,26]],"date-time":"2024-07-26T00:00:00Z","timestamp":1721952000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["12101378","20210302124548"],"award-info":[{"award-number":["12101378","20210302124548"]}]},{"name":"Shanxi Provincial Research Foundation for Basic Research, China","award":["12101378","20210302124548"],"award-info":[{"award-number":["12101378","20210302124548"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Random matrix series are a significant component of random matrix theory, offering rich theoretical content and broad application prospects. In this paper, we propose modified versions of tail bounds for random matrix series, including matrix Gaussian (or Rademacher) and sub-Gaussian and infinitely divisible (i.d.) series. Unlike present studies, our results depend on the intrinsic dimension instead of ambient dimension. In some cases, the intrinsic dimension is much smaller than ambient dimension, which makes the modified versions suitable for high-dimensional or infinite-dimensional setting possible. In addition, we obtain the expectation bounds for random matrix series based on the intrinsic dimension.<\/jats:p>","DOI":"10.3390\/e26080633","type":"journal-article","created":{"date-parts":[[2024,7,26]],"date-time":"2024-07-26T13:04:59Z","timestamp":1721999099000},"page":"633","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Optimized Tail Bounds for Random Matrix Series"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7527-0003","authenticated-orcid":false,"given":"Xianjie","family":"Gao","sequence":"first","affiliation":[{"name":"Department of Basic Sciences, Shanxi Agricultural University, Jinzhong 030801, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mingliang","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jinming","family":"Luo","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,7,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1561\/0100000001","article-title":"Random matrix theory and wireless communications","volume":"1","author":"Tulino","year":"2004","journal-title":"Found. 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