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.
On the spectral norm of Rademacher matrices
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abstract
We discuss two-sided non-asymptotic bounds for the mean spectral norm of nonhomogenous weighted Rademacher matrices. We show that the recently formulated conjecture holds up to $\log \log \log n$ factor for arbitrary $n\times n$ Rademacher matrices and the triple logarithm may be eliminated for matrices with $\{0,1\}$-coefficients.
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2025 1verdicts
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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.