A note on q-Gaussians and non-Gaussians in statistical mechanics
Abstract
The sum of N sufficiently strongly correlated random variables will not in general be Gaussian distributed in the limit N∞. 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)×[1-(1-q)x2]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.
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