Journal of Statistical Physics

, Volume 157, Issue 4–5, pp 915–930 | Cite as

An Application of the Renormalization Group Method to Stable Limit Laws

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Abstract

Let \((X_n)_{n=1}^{\infty }\) be a sequence of independent identically distributed random variables. We study the normalized partial sums and the corresponding renormalization group flow in the space of probability densities. We prove the convergence to stable limit laws under suitable assumptions on the initial density.

Keywords

Stable limit law Renormalization group Random variable  

Notes

Acknowledgments

Y. G. Sinai was supported by NSF Grant DMS 1265547. D. Li was supported in part by an Nserc discovery grant. We thank the anonymous referees for very helpful comments and suggestions.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of British ColumbiaVancouverCanada
  2. 2.Mathematics DepartmentPrinceton UniversityPrincetonUSA
  3. 3.Landau Institute of Theoretical PhysicsMoscowRussia

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