Scholarlink

<p>Let <i>M</i> be an <i>n</i>×<i>n</i> matrix with iid subgaussian entries with mean 0 and variance 1 and let <i>σ</i><sub><i>n</i></sub>(<i>M</i>) denote the least singular value of <i>M</i>. We prove that <Equation ID="Equa"> <MediaObject> <ImageObject Color="BlackWhite" FileRef="39_2025_707_Article_Equa.gif" Format="GIF" Height="24" Rendition="HTML" Resolution="72" Type="Linedraw" Width="303" /> </MediaObject> <EquationSource Format="TEX">\( \mathbb{P}\big( \sigma _{n}(M) \leqslant \varepsilon n^{-1/2} \big) = (1+o(1)) \varepsilon + e^{- \Omega (n)} \)</EquationSource> </Equation> for all 0⩽<i>ε</i>≪1. This resolves, up to a 1+<i>o</i>(1) factor, a seminal conjecture of Spielman and Teng.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

On the Spielman-Teng Conjecture

  • 期刊论文

  • 发表日期：

    2025年2月13日

查看全文
  • Ashwin Sah,
  • Julian Sahasrabudhe,
  • Mehtaab Sawhney

摘要

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.