Generalized Central Limit Theorem and Renormalization Group

Details Generalized Central Limit Theorem and Renormalization Group Generalized Central Limit Theorem and Renormalization Group

2010-09-15

arxiv.org/abs/1009.2899v1

Physics

Mathematical Physics

16 pages, to appear in J. Stat. Phys

Scientific paper

We introduce a simple instance of the renormalization group transformation in the Banach space of probability densities. By changing the scaling of the renormalized variables we obtain, as fixed points of the transformation, the L\'evy strictly stable laws. We also investigate the behavior of the transformation around these fixed points and the domain of attraction for different values of the scaling parameter. The physical interest of a renormalization group approach to the generalized central limit theorem is discussed.

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