Generalized-generalized entropies and limit distributions

Limit distributions are not limited to uncorrelated variables but can be constructively derived for a large class of correlated random variables, as was shown e.g. in the context of large deviation theory [1], and recently in a very general setting by Hilhorst and Schehr [2]. At the same time it has been conjectured, based on numerical evidence, that several limit distributions originating from specific correlated random processes follow q-Gaussians. It could be shown that this is not the case for some of these situations, and more complicated limit distributions are necessary. In this work we...