Yi Han

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math.PR2025

Repeated singular values of a random symmetric matrix and decoupled singular value estimates

Yi Han

Let $A_{n}$ be a random symmetric matrix with Bernoulli ${\pm 1}$ entries. For any $κ > 0$ and two real numbers $λ_{1}, λ_{2}$ with a separation $∣ λ_{1} - λ_{2} ∣ \geq κ n^{1/2}$ and both lying in…

math.PR2025

Simplicity of singular value spectrum of random matrices and two-point quantitative invertibility

Yi Han

Let $A$ be an $n \times n$ random matrix with independent, identically distributed mean 0, variance 1 subgaussian entries. We prove that $$ \mathbb{P}(A\text{ has distinct singular…

math.PR2024

The smallest singular value for rectangular random matrices with Lévy entries

Yi Han

Let $X = (x_{ij}) \in R^{N \times n}$ be a rectangular random matrix with i.i.d. entries (we assume $N / n \to a > 1$ ), and denote by $σ_{min} (X)$ its smallest singular valu…