An elementary renormalization-group approach to the generalized central limit theorem and extreme value distributions

Generalized Central Limit Theorem and Extreme Value Statistics

Extreme-value distributions and renormalization group.

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 approa...

Renormalization Group Approach to Generalized Cosmological models

It is widely accepted that Einstein’s general theory of relativity is an effective four-dimensional theory at lower energies and that it needs modifications at high energies. In the cosmological context, this break down of the theory results in a modification of the Friedmann equation with important consequences in the dynamical evolution at early times (see for example, [1, 2]). There has been...

Characteristics of Generalized Extreme Value Distributions

This note is concerned with joint probability distributions whose one-dimensional marginal distributions are Extreme Value Type 1 (EV1); i.e., Prob(Uj # uj) = exp(-exp(:(uj-vj)), where the vj are location parameters and : is a common scale factor. Call these Generalized Extreme Value (GEV) distributions. GEV distributions have application in the study of discrete choice behavior, and were initi...

A NUMERICAL RENORMALIZATION GROUP APPROACH FOR AN ELECTRON-PHONON INTERACTION

A finite chain calculation in terms of Hubbard X-operators is explored by setting up a vibronic Harniltonian. The model conveniently transformed into a form so that in the case of strong coupling a numerical renormalization group approach is applicable. To test the technique, a one particle Green function is calculated for the model Harniltonian