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Achintya Raya Polavarapu

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Preprint Aug 2026

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

Let $A=(\xi_{ij})$ be an $n\times n$ random matrix with independent, not necessarily identically distributed, real entries satisfying \[ \mathbb E\xi_{ij}=0,\qquad \mathbb E\xi_{ij}^{2}=1,\qquad \sup_{z\in\mathbb R}\mathbb P(|\xi_{ij}-z|0$ and $b\in(0,1)$. We prove that, for every $\delta\in(0,1)$, there are constants...

Manuel Fernández, Achintya Raya Polavarapu · 0 citations

Preprint Jul 2026

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

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 exists $\kappa \in (0, 1)$ such that the entries of $A$ satisfy $$ \max_{i,j}\sup_{u \in \mathbb{R}} \mathbb{P}(\lvert a_{ij} - u\rvert<1) \le...

B. Letwin, Achintya Raya Polavarapu · 0 citations