Norms of randomized circulant matrices

We investigate two-sided bounds for operator norms of random matrices with nonhomogenous independent entries. We formulate a lower bound for Rademacher matrices and conjecture that it may be reversed up to a universal constant. We show that our conjecture holds up to log log n factor for randomized n ?? n circulant matrices and that the double logarithm may be eliminated under some mild additional assumptions on the coefficients.