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The nonextensivity parameter q occurring in some of the applications of Tsallis statistics (known also as index of the corresponding Levy distribution) is shown to be given, in the q>1 case, entirely by the fluctuations of the parameters of the usual exponential distribution.

ALICE is the heavy-ion experiment at the CERN Large Hadron Collider. The experiment continuously took data during the first physics campaign of the machine from fall 2009 until early 2013, using proton and lead-ion beams. In this paper we describe the running environment and the data handling procedures, and discuss the performance of the ALICE detectors and analysis methods for various physics observables.

This publication describes the methods used to measure the centrality of inelastic Pb-Pb collisions at a center-of-mass energy of 2.76 TeV per colliding nucleon pair with ALICE. The centrality is a key parameter in the study of the properties of QCD matter at extreme temperature and energy density, because it is directly related to the initial overlap region of the colliding nuclei. Geometrical properties of the collision, such as the number of participating nucleons and the number of binary nucleon-nucleon collisions, are deduced from a Glauber model with a sharp impact parameter selection and shown to be consistent with those extracted from the data. The centrality determination provides a tool to compare ALICE measurements with those of other experiments and with theoretical calculations.