Global fluctuations and Gumbel statistics

We explain how the statistics of global observables in correlated systems can be related to extreme value problems and to Gumbel statistics. This relationship then naturally leads to the emergence of the generalized Gumbel distribution G_a(x), with a real index a, in the study of global fluctuations. To illustrate these findings, we introduce an exactly solvable nonequilibrium model describing an energy flux on a lattice, with local dissipation, in which the fluctuations of the global energy are precisely described by the generalized Gumbel distribution.