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Extremal random matrices with independent entries and matrix superconcentration inequalities
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We prove nonasymptotic matrix concentration inequalities for the spectral norm of (sub)gaussian random matrices with centered independent entries that capture fluctuations at the Tracy-Widom scale. This considerably improves previous bounds in this setting due to Bandeira and Van Handel, and establishes the best possible tail behavior for random matrices with an arbitrary variance pattern. These bounds arise from an extremum problem for nonhomogeneous random matrices: among all variance patterns with a given sparsity parameter, the moments of the random matrix are maximized by block-diagonal matrices with i.i.d. entries in each block. As part of the proof, we obtain sharp bounds on large moments of Gaussian Wishart matrices.
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Cited by 2 Pith papers
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Operator $\ell_p\to\ell_q$ norms of Gaussian matrices
For Gaussian matrices with arbitrary variance profiles, the expected ℓ_p to ℓ_q norm is comparable, up to constants depending only on p and q, to the sum of the largest row and column norms plus the expected maximum entry.
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Spectral radius concentration for inhomogeneous random matrices with independent entries
For inhomogeneous random matrices, the spectral radius is bounded by the variance row/column sums up to the optimal sparsity (log n)^{-1/2}.
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