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On the spectral norm of Rademacher matrices

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arxiv 2405.13656 v2 pith:NWMVIP7P submitted 2024-05-22 math.PR math.FA

classification math.PRmath.FA
keywords matricesrademachernormspectralarbitraryboundscoefficientsconjecture
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Operator $\ell_p\to\ell_q$ norms of Gaussian matrices

    math.PR 2025-02 accept novelty 8.0 of 10

    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.

  2. A Geometric Perspective on the Injective Norm of Sums of Random Tensors

    math.PR 2024-11 conditional novelty 6.0 of 10

    New geometric proof establishes nearly optimal bounds on the ℓ_p injective norm of sums of random tensors for all p ≥ 2 and tensor order r.

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