On the Spielman-Teng Conjecture
Author(s)
Sah, Ashwin; Sahasrabudhe, Julian; Sawhney, Mehtaab
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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.
Date issued
2025-02-13Department
Massachusetts Institute of Technology. Department of MathematicsJournal
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