Achintya Raya Polavarapu

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math.PR2026

Intermediate Singular Values of Random Matrices under Second-Moment and Anti-Concentration Assumptions

Achintya Raya Polavarapu, Manuel Fernandez

Let $A = (ξ_{ij})$ be an $n \times n$ random matrix with independent, not necessarily identically distributed, real entries satisfying \[ \mathbb Eξ_{ij}=0,\qquad \mathbb Eξ_{ij}^{2}=…

math.PR2026

On the smallest singular value of the product of random and deterministic matrices

Brayden Letwin, Achintya Raya Polavarapu

Let $A = (a_{ij})$ be an $n \times n$ real-valued random matrix with independent, mean-zero, variance-one entries whose fourth moments are uniformly at most $K$ . Suppose that there ex…

math.PR2026

Exponential Rank Bounds for Random Matrices

Achintya Raya Polavarapu

Fix $b \in (0, 1)$ , let $1 \leq k \leq n$ , and let $A = (A_{ij})$ be an $n \times n$ random matrix with independent real entries satisfying $$ \sup_{x\in\mathbb{R}}\mathbb{P}\{A_{ij}=x\}\l…