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Extreme-value distributions and renormalization group

Iván Calvo*

Juan C. Cuchí†

J. G. Esteve‡ and Fernando Falceto§

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

  • Departament d’Enginyeria Agroforestal, Universitat de Lleida, 25198 Lleida, Spain

  • Departamento de Física Teórica, Universidad de Zaragoza, 50009 Zaragoza, Spain and Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), 50009 Zaragoza, Spain

  • *ivan.calvo@ciemat.es
  • †cuchi@eagrof.udl.cat
  • ‡Corresponding author: esteve@unizar.es
  • §falceto@unizar.es
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Phys. Rev. E 86, 041109 – Published 8 October, 2012

DOI: https://doi.org/10.1103/PhysRevE.86.041109

Abstract

In the classical theorems of extreme value theory the limits of suitably rescaled maxima of sequences of independent, identically distributed random variables are studied. The vast majority of the literature on the subject deals with affine normalization. We argue that more general normalizations are natural from a mathematical and physical point of view and work them out. The problem is approached using the language of renormalization-group transformations in the space of probability densities. The limit distributions are fixed points of the transformation and the study of its differential around them allows a local analysis of the domains of attraction and the computation of finite-size corrections.

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Outline

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Phys. Rev. E 86, 041109– Published 8 October, 2012
  • Received 11 July 2012

©2012 American Physical Society

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