Global fluctuations and Gumbel statistics

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.

4 pages, 3 figures; final version with minor changes

References in corpus (15)

• Universality Classes for Extreme Value Statistics
• Universal Fluctuations in Correlated Systems
• 1/f Noise and Extreme Value Statistics
• Injected Power Fluctuations in Langevin Equation
• Magnetic fluctuations in the classical XY model: the origin of an exponential tail in a complex system
• Roughness distributions for 1/f^alpha signals
• Statistics of extremal intensities for Gaussian interfaces
• Fluctuations in finite critical and turbulent systems
• Universal Fluctuations of the Danube Water Level: a Link with Turbulence, Criticality and Company Growth
• Universal fluctuations and extreme value statistics
• Criterion for universality class independent critical fluctuations: example of the 2D Ising model
• Universal Magnetic Fluctuations with a Field Induced Length Scale
• Scaling and universality of critical fluctuations in granular gases
• Relevance of soft modes for order parameter fluctuations in the Two-Dimensional XY model
• Scaling and Commonality in Anomalous Fluctuation Statistics in Models for Turbulence and Ferromagnetism

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