On the Spielman-Teng Conjecture
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Author(s)
Sah, Ashwin
Sahasrabudhe, Julian
Sawhney, Mehtaab
Date Issued
February 13, 2025
Journal
Geometric and Functional Analysis
Publisher
Springer International Publishing
Citation
Sah, A., Sahasrabudhe, J. & Sawhney, M. On the Spielman-Teng Conjecture. Geom. Funct. Anal. 35, 633–671 (2025).
Version
Author's final manuscript
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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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.
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DOI of Published Version
https://doi.org/10.1007/s00039-025-00707-z
