Notice that in order to conclude that the deviation from 0 is bounded by with high probability, we need to choose a number of samples formula_38 proportional to the logarithm of formula_39. In general, unfortunately, a dependence on formula_40 is inevitable: take for example a diagonal random sign matrix of dimension formula_41. The operator norm of the sum of "t" independent samples is precisely the maximum deviation among "d" independent random walks of length "t". In order to achieve a fixed bound on the maximum deviation with constant probability, it is easy to see that "t" should grow logarithmically with "d" in this scenario.