title: Extreme-value distributions and renormalization group.
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.
authors.affiliation: Laboratorio Nacional de Fusión, Asociación EURATOM-CIEMAT, 28040 Madrid, Spain. ivan.calvo@ciemat.es
authors.forename: Iván
authors.initials: I
authors.lastname: Calvo
authors.forename: Juan C
authors.initials: JC
authors.lastname: Cuchí
authors.forename: J G
authors.initials: JG
authors.lastname: Esteve
authors.forename: Fernando
authors.initials: F
authors.lastname: Falceto
mesh_terms: D000465:Algorithms; D019295:Computational Biology / Q000379:methods; D003198:Computer Simulation; D015233:Models, Statistical; D008962:Models, Theoretical; D010825:Physics / Q000379:methods; D011336:Probability