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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.17741 |
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Table of Contents:
- Let $M_n$ be an $n \times n$ random matrix with i.i.d. sparse discrete entries. In this paper, we develop a simple framework to solve the approximate Spielman-Teng theorem for $M_n$, which has the following form: There exist constants $C, c>0$ such that for all $η\geq 0$, $\textbf{P}\left(s_n\left(M_n\right) \leq η\right) \lesssim n^C η+\exp \left(-n^c\right)$. As an application, we give an approximate Spielman-Teng theorem for $M_n$ whose entries are $μ-$lazy random variables, extending previous work by Tao and Vu.