A note on q-Gaussians and non-Gaussians in statistical mechanics

The sum of N sufficiently strongly correlated random variables will not in general be Gaussian distributed in the limit N -> infinity. We revisit examples of sums x that have recently been put forward as instances of variables obeying a q-Gaussian law, that is, one of type cst x [1 -( 1 - q) x(2)](1/(1-q)). We show by explicit calculation that the probability distributions in the examples are actually analytically different from q-Gaussians, in spite of numerically resembling them very closely. Although q-Gaussians exhibit many interesting properties, the examples investigated do not support the idea that they play a special role as limit distributions of correlated sums.