  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.
