Séminaire de groupe
|Generalised extreme value statistics and sums of correlated random variables|
|Laboratoire des Colloïdes, Verres et Nanomatériaux - UMR 5587, Montpellier|
|jeudi 13 septembre 2012 , 11h05|
|Salle de séminaire du groupe de Physique Statistique|
I will show that extreme value statistics -the statistics of the k-th largest value among a large set of random variables- can be mapped onto a problem of random sums. This allows to identify classes of non-identical and (generally) correlated random variables with a sum distributed according to one of the three (k-dependent) asymptotic distributions of extreme value statistics, namely the Gumbel, Frechet and Weibull distributions. These classes, as well as the limit distributions, are naturally extended to real values of k, thus providing a clear interpretation to the onset of Gumbel distributions with non-integer index k in the statistics of global observables. This is one of the very few known generalisations of the central limit theorem to non-independent random variables. Finally, in the context of a simple physical model, I will relate the index k to the ratio of the correlation length to the system size, which remains finite in strongly correlated systems.