One-sided Gaussian tail for the smallest singular value: $\mathbb P\{s_{\min}(A)\le\sqrt N-\sqrt n-u\}\le e^{-u^2/2}$

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One-sided Gaussian tail for the smallest singular value: $\mathbb P\{s_{\min}(A)\le\sqrt N-\sqrt n-u\}\le e^{-u^2/2}$ · Prove2Me