| dc.contributor.author | Sah, Ashwin | |
| dc.contributor.author | Sahasrabudhe, Julian | |
| dc.contributor.author | Sawhney, Mehtaab | |
| dc.date.accessioned | 2025-06-16T19:46:47Z | |
| dc.date.available | 2025-06-16T19:46:47Z | |
| dc.date.issued | 2025-02-13 | |
| dc.identifier.uri | https://hdl.handle.net/1721.1/159423 | |
| dc.description.abstract | Let M be an n×n matrix with iid subgaussian entries with mean 0 and variance 1 and let σn(M) denote the least singular value of M. We prove that $$ \mathbb{P}\big( \sigma _{n}(M) \leqslant \varepsilon n^{-1/2} \big) = (1+o(1)) \varepsilon + e^{- \Omega (n)} $$ for all 0⩽ε≪1. This resolves, up to a 1+o(1) factor, a seminal conjecture of Spielman and Teng. | en_US |
| dc.publisher | Springer International Publishing | en_US |
| dc.relation.isversionof | https://doi.org/10.1007/s00039-025-00707-z | en_US |
| dc.rights | Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. | en_US |
| dc.source | Springer International Publishing | en_US |
| dc.title | On the Spielman-Teng Conjecture | en_US |
| dc.type | Article | en_US |
| dc.identifier.citation | Sah, A., Sahasrabudhe, J. & Sawhney, M. On the Spielman-Teng Conjecture. Geom. Funct. Anal. 35, 633–671 (2025). | en_US |
| dc.contributor.department | Massachusetts Institute of Technology. Department of Mathematics | en_US |
| dc.relation.journal | Geometric and Functional Analysis | en_US |
| dc.eprint.version | Author's final manuscript | en_US |
| dc.type.uri | http://purl.org/eprint/type/JournalArticle | en_US |
| eprint.status | http://purl.org/eprint/status/PeerReviewed | en_US |
| dc.date.updated | 2025-03-27T13:47:54Z | |
| dc.language.rfc3066 | en | |
| dc.rights.holder | The Author(s), under exclusive licence to Springer Nature Switzerland AG | |
| dspace.embargo.terms | Y | |
| dspace.date.submission | 2025-03-27T13:47:54Z | |
| mit.journal.volume | 35 | en_US |
| mit.license | PUBLISHER_POLICY | |
| mit.metadata.status | Authority Work and Publication Information Needed | en_US |
