A note on q-Gaussians and non-Gaussians in statistical mechanics
نویسنده
چکیده
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, even though numerically resembling them very closely. We find no indication supporting the idea that qGaussians play a special role as limit distributions of correlated sums.
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