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Analysis shows singular values of random matrices exhibit tighter deviation inequalities, suggesting improved bounds.
Let [Formula: see text] be an [Formula: see text] random matrix with i.i.d. entries. This paper studies the deviation inequality of [Formula: see text], the [Formula: see text]-th smallest singular value of [Formula: see text]. In particular, when the entries of [Formula: see text] are subgaussian, we show that for any [Formula: see text] and [Formula: see text] [Formula: see text] This result improves an existing result due to Nguyen, which is a deviation inequality of [Formula: see text] with [Formula: see text] decay.
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Dai et al. (2026) studied this question.
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