The least singular value of a random symmetric matrix

Autor: Marcelo Campos, Matthew Jenssen, Marcus Michelen, Julian Sahasrabudhe
Jazyk: angličtina
Rok vydání: 2024
Předmět:
Zdroj: Forum of Mathematics, Pi, Vol 12 (2024)
Druh dokumentu: article
ISSN: 2050-5086
DOI: 10.1017/fmp.2023.29
Popis: Let A be an $n \times n$ symmetric matrix with $(A_{i,j})_{i\leqslant j}$ independent and identically distributed according to a subgaussian distribution. We show that $$ \begin{align*}\mathbb{P}(\sigma_{\min}(A) \leqslant \varepsilon n^{-1/2} ) \leqslant C \varepsilon + e^{-cn},\end{align*} $$
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