The Number of Inversions and the Major Index of Permutations are Asymptotically Joint-Independently-Normal

Human statistics are numerical attributes defined on humans, for example, longevity, height, weight, IQ, and it is well-known, at least empirically, that these are, each separately, asymptotically normal, which means that if you draw a histogram with the statistical data, it would look like a bell-curve. It is also true that they are usually joint-asymptotically-normal, but usually not independently so. But if you compute empirically the correlation matrix, you would get, asymptotically (i.e. for “large” populations) that they are close to being distributed according to a multivariate (generalized) Gaussian exp(−Q(x1, x2, ...)) with Q(x1, x2, . . .) a certain quadratic form that can be deduced from the correlation matrix.