On the spectral norm of Rademacher matrices

TL;DR

This paper provides non-asymptotic bounds on the spectral norm of Rademacher matrices, confirming a conjecture up to a triple logarithmic factor and improving bounds for matrices with binary coefficients.

Contribution

It establishes bounds on the spectral norm of Rademacher matrices, confirming a conjecture and refining results for matrices with binary entries.

Findings

Conjecture holds up to log log log n factor for general Rademacher matrices.

Triple logarithm factor can be eliminated for matrices with {0,1} coefficients.

Provides non-asymptotic bounds for the spectral norm.

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.