The smallest singular value of inhomogeneous square random matrices

Galyna V. Livshyts, Konstantin Tikhomirov, Roman Vershynin

We show that for an $n\times n$ random matrix $A$ with independent uniformly anti-concentrated entries, such that $\mathbb{E}||A|{|}_{HS}^2\le K{n}^2$, the smallest singular value $…