viewed as an optimization problem over the unit cube? More generally, we can ask similar questions over convex bodies other than the unit cube. For instance, the following inequality is due to Naor and Schechtman and independently due to Guruswami et al: For every matrix and every , where The constant is sharp in the inequality. Stirling's formula implies that as . See also Pisier–Ringrose inequality References External links (NB: the historical part is not exact there.) Theorems in functional analysis Inequalities