On the spectral norm of Rademacher matrices

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.