M. Fernández

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math.PR2025

On the Smallest Singular Value of Log-Concave Random Matrices

Manuel Fernandez, Galyna V. Livshyts, Stephanie Mui

Let $A$ be an $N \times n$ random matrix whose entries are coordinates of an isotropic log-concave random vector in $R^{N n}$ . We prove sharp lower tail estimates for the sm…

math.PR2025

The smallest singular value of inhomogenous random rectangular matrices

Max Dabagia, Manuel Fernandez

Let $A \in R^{N \times n}$ ( $N \geq n$ ) be a random matrix with with independent entries that have mean 0 variance 1 and bounded $2 + I^^{2}$ moment. We show that the smallest s…

math.PR2025

A distance theorem for inhomogenous random rectangular matrices

Manuel Fernandez

Let $A \in R^{n \times (n - d)}$ be a random matrix with independent uniformly anti-concentrated entries satisfying $E ∣ A ∣_{H S}^{2} \leq K n (n - d)$ and let…