title: Central Limit Theorems under additive deformations.
abstract: Additive deformations of statistical systems arise in various areas of physics. Classical central limit theory is then no longer applicable, even when standard independence assumptions are preserved. This paper investigates ways in which deformed algebraic operations lead to distinctive central limit theory. We establish some general central limit results that are applicable to a range of examples arising in nonextensive statistical mechanics, including the addition of momenta and velocities via Kaniadakis addition, and Tsallis addition. We also investigate extensions to random additive deformations, and find evidence (based on simulation studies) for a universal limit specific to each statistical system.
authors: Department of Statistics, University of Minnesota, 313 Ford Hall, 224 Church St SE, Minneapolis, MN 55455, USA.
authors: Daniel J
authors: DJ
authors: Eck
authors: Department of Biostatistics, Columbia University, 722 West 168th St. NY, NY 10032, USA.
authors: Ian W
authors: IW
authors: McKeague
keywords: Kaniadakis addition; Probability on Lie groups; Tsallis entropy