Han Huang

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math.PR2026

Well-invertible column subsets of sparse matrices are rare

Han Huang, Mark Rudelson, Konstantin Tikhomirov

A random $n \times k$ matrix $S$ is an \emph{ $(r, I^\pm)$ -oblivious subspace injection} (OSI) if $E ∥ S^{⊤} x ∥_{2}^{2} = ∥ x ∥_{2}^{2}$ for every $x \in R^{n}$ , and for every fixed…

math.PR2025

Rank of Sparse Bernoulli Matrices

Han Huang

Let $A_{n}$ be an $n \times n$ random matrix with i.i.d Bernoulli( $p$ ) entries. For a fixed positive integer $I^^{2}$ , suppose $p$ satisfies $\frac{lo g ( n )}{n} \leq p \leq c_{I^}^{2}$ w…