Why is the detection of q-Gaussian behavior such a common occurrence?

Abstract : q-Gaussian behavior is often encountered in quite distinct settings. A possible explanation is here given with reference to experimental scenarios in which data are gathered using a set-up that performs a normalization preprocessing. We show that the ensuing normalized input, as recorded by the measurement device, will always be q-Gaussian distributed if the incoming data exhibit elliptical symmetry, a rather common feature. Moreover, we find that in these circumstances, the value of the associated parameter q can be deduced from the normalization technique that characterizes the device. Finally, one concludes from the above remarks that great care should be exercised when empirically detecting q-Gaussian behavior. As an example, Gaussian data (the most common situation) will appear, after normalization, in the guise of q-Gaussian records. (c) 2008 Elsevier B.V. All rights reserved.
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Christophe Vignat, A. Plastino. Why is the detection of q-Gaussian behavior such a common occurrence?. Physica A: Statistical Mechanics and its Applications, Elsevier, 2009, 388 (5), pp.601-608. 〈10.1016/j.physa.2008.11.001〉. 〈hal-00693560〉



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