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Our results apply to the high-dimensional regime n,d\u2192\u221e and d\/n\u2192\u221e (or d\/n\u21920) and generalize earlier work that focused on the proportional asymptotics n,d\u2192\u221e, d\/n\u2192\u03b4\u2208(0,\u221e). We outline an interesting signal strength regime in which d\/n\u2192\u221e and partial recovery is possible for the left singular vectors while impossible for the right singular vectors. We illustrate the general theory by deriving consequences for Gaussian mixture clustering and carrying out a numerical study on genomics data.<\/jats:p>","DOI":"10.1214\/24-aos2400","type":"journal-article","created":{"date-parts":[[2024,10,4]],"date-time":"2024-10-04T01:49:23Z","timestamp":1728006563000},"page":"1460-1484","source":"Crossref","is-referenced-by-count":3,"title":["Fundamental limits of low-rank matrix estimation with diverging aspect ratios"],"prefix":"10.1214","volume":"52","author":[{"given":"Andrea","family":"Montanari","sequence":"first","affiliation":[{"name":"Department of Statistics and Department of Mathematics, Stanford University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuchen","family":"Wu","sequence":"additional","affiliation":[{"name":"Department of Statistics and Data Science, the Wharton School, University of Pennsylvania"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"108","reference":[{"key":"10","doi-asserted-by":"publisher","unstructured":"Barbier, J.<\/small> and Macris, N.<\/small> (2019). 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