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Generalized Central Limit Theorem and Renormalization Group

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Abstract

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 Lévy 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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Authors and Affiliations

  1. Departamento de Física Teórica, Universidad de Zaragoza, 50009, Zaragoza, Spain

    José G. Esteve & Fernando Falceto

  2. Laboratorio Nacional de Fusión, Asociación EURATOM-CIEMAT, 28040, Madrid, Spain

    Iván Calvo

  3. Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), 50009, Zaragoza, Spain

    Iván Calvo, José G. Esteve & Fernando Falceto

  4. Departament d’Enginyeria Agroforestal, Universitat de Lleida, 25198, Lleida, Spain

    Juan C. Cuchí

Authors
  1. Iván Calvo
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  2. Juan C. Cuchí
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  3. José G. Esteve
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  4. Fernando Falceto
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Correspondence to Fernando Falceto.

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Calvo, I., Cuchí, J.C., Esteve, J.G. et al. Generalized Central Limit Theorem and Renormalization Group. J Stat Phys 141, 409–421 (2010). https://doi.org/10.1007/s10955-010-0065-y

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  • DOI: https://doi.org/10.1007/s10955-010-0065-y

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