Journal of Statistical Physics

, Volume 141, Issue 3, pp 409–421 | Cite as

Generalized Central Limit Theorem and Renormalization Group

  • Iván Calvo
  • Juan C. Cuchí
  • José G. Esteve
  • Fernando Falceto
Article

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.

Keywords

Central limit theorems Stable distributions Characteristic functions Renormalization group methods 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Iván Calvo
    • 2
    • 3
  • Juan C. Cuchí
    • 4
  • José G. Esteve
    • 1
    • 3
  • Fernando Falceto
    • 1
    • 3
  1. 1.Departamento de Física TeóricaUniversidad de ZaragozaZaragozaSpain
  2. 2.Laboratorio Nacional de FusiónAsociación EURATOM-CIEMATMadridSpain
  3. 3.Instituto de Biocomputación y Física de Sistemas Complejos (BIFI)ZaragozaSpain
  4. 4.Departament d’Enginyeria AgroforestalUniversitat de LleidaLleidaSpain

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