Global fluctuations and Gumbel statistics

TL;DR

This paper links global observable fluctuations in correlated systems to Gumbel statistics, demonstrating how the generalized Gumbel distribution naturally arises in such contexts, supported by an exactly solvable nonequilibrium lattice model.

Contribution

It establishes a theoretical connection between global fluctuations and Gumbel statistics, introducing a solvable model that exemplifies this relationship.

Findings

Global fluctuations follow generalized Gumbel distribution

The model precisely describes energy fluctuation statistics

Gumbel statistics emerge naturally in correlated systems

Abstract

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.