Extreme value distributions and Renormalization Group

Details Extreme value distributions and Renormalization Group Extreme value distributions and Renormalization Group

2011-09-27

arxiv.org/abs/1109.5841v1

Physics

Mathematical Physics

16 pages, 5 figures

Scientific paper

In the classical theorems of extreme value theory the limits of suitably rescaled maxima of sequences of independent, identically distributed random variables are studied. So far, only affine rescalings have been considered. We show, however, that more general rescalings are natural and lead to new limit distributions, apart from the Gumbel, Weibull, and Fr\'echet families. 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 the differential around them allows a local analysis of the domains of attraction and the computation of finite-size corrections.

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