# Universal fluctuations and extreme-value statistics

@article{Dahlstedt2001UniversalFA, title={Universal fluctuations and extreme-value statistics}, author={Kajsa Dahlstedt and Henrik Jeldtoft Jensen}, journal={Journal of Physics A}, year={2001}, volume={34}, pages={11193-11200} }

We study the effect of long-range algebraic correlations on extreme-value statistics and demonstrate that correlations can produce a limit distribution which is indistinguishable from the ubiquitous Bramwell–Holdsworth–Pinton distribution. We also consider the square-width fluctuations of the avalanche signal. We find, as recently predicted by Antal et al for logarithmic correlated 1/f signals, that these fluctuations follow the Fisher–Tippett–Gumbel distribution from uncorrelated extreme-value…

## 41 Citations

Global fluctuations and Gumbel statistics.

- PhysicsPhysical review letters
- 2005

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.

Generalized extreme value statistics and sum of correlated variables

- Mathematics
- 2006

We show that generalized extreme value statistics—the statistics of the kth largest value among a large set of random variables—can be mapped onto a problem of random sums. This allows us to identify…

Extreme value statistics in records with long-term persistence.

- Mathematics, Environmental SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2006

It is found numerically that the integrated distribution function of the maxima converges to a Gumbel distribution for large R similar to uncorrelated signals, and that conditional mean maxima and conditional maxima distributions should be considered for an improved extreme event prediction.

Extreme fluctuations in noisy task-completion landscapes on scale-free networks.

- Computer ScienceChaos
- 2007

This work presents large-scale simulation results using the exact algorithmic rules, supported by mean-field arguments based on a coarse-grained description, of extreme fluctuations in noisy task-completion landscapes, such as those emerging in synchronized distributed-computing networks, or generic causally constrained queuing networks, with scale-free topology.

Distribution of extremes in the fluctuations of two-dimensional equilibrium interfaces.

- MathematicsPhysical review letters
- 2005

The standardized form of P(m) does not depend on N or K, but shows a good agreement with Gumbel's first asymptote distribution with a particular noninteger parameter, and the effects of the correlations among individual fluctuations on the extreme value statistics are discussed.

Non-Gaussian Fluctuations in Biased Resistor Networks: Size Effects versus Universal Behavior

- Physics
- 2005

We study the distribution of the resistance fluctuations of biased resistor networks in nonequilibrium steady states. The stationary conditions arise from the competition between two stochastic and…

Statistics of extremal intensities for Gaussian interfaces.

- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2003

The extremal Fourier intensities are studied for stationary Edwards-Wilkinson-type, Gaussian, interfaces with power-law dispersion and it is found that the maximal intensity does not coincide with the distribution of the integrated power spectrum, nor does it obey any of the known extreme statistics limit distributions.

CYCLES AND UNIVERSALITY IN SUNSPOT NUMBER FLUCTUATIONS

- Physics
- 2009

We analyze the famous Wolf's sunspot numbers. Surprisingly, we discovered that the distribution of the sunspot number fluctuations for both the ascending and descending phases is close to the…

EXTREME FLUCTUATIONS IN SMALL-WORLD-COUPLED AUTONOMOUS SYSTEMS WITH RELAXATIONAL DYNAMICS

- Computer Science
- 2005

This work investigates to what extent small-world couplings (extending the original local relaxational dynamics through the random links) lead to the suppression of extreme fluctuations in the synchronization landscape of natural and artificial coupled multi-component systems.

The Statistics of Return Intervals, Maxima, and Centennial Events Under the Influence of Long-Term Correlations

- Mathematics
- 2011

We review our studies of the statistics of return intervals and extreme events (block maxima) in long-term correlated data sets, characterized by a power-law decaying autocorrelation function with…

## References

SHOWING 1-8 OF 8 REFERENCES

Universal fluctuations in correlated systems

- PhysicsPhysical review letters
- 2000

It is demonstrated that this function describes the fluctuations of global quantities in other correlated equilibrium and nonequilibrium systems, including a coupled rotor model, Ising and percolation models, models of forest fires, sandpiles, avalanches, and granular media in a self-organized critical state.

Fluctuations in finite critical and turbulent systems.

- PhysicsPhysical review letters
- 2001

It is shown that hyperscaling and finite- size scaling imply that the probability distribution of the order parameter in finite-size critical systems exhibit data collapse, and an explanation for recent observations that the probabilities of turbulent power fluctuations in closed flows is the same as that of the harmonic 2DXY model is proposed.

Universality of rare fluctuations in turbulence and critical phenomena

- PhysicsNature
- 1998

A statistical treatment of three-dimensional turbulent flow continues to pose a challenge to theorists,. One suggestion invokes an analogy with equilibrium phase transitions. Here we approach this…

Glass transition of a particle in a random potential, front selection in nonlinear renormalization group, and entropic phenomena in Liouville and sinh-Gordon models.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2001

Applications to Dirac fermions in random magnetic fields at criticality reveal a peculiar "quasilocalized" regime (corresponding to the glass phase for the particle), where eigenfunctions are concentrated over a finite number of distant regions, and allow us to recover the multifractal spectrum in the delocalized regime.

Self-organized pinning and interface growth in a random medium.

- PhysicsPhysical review letters
- 1992

A new universality class of growth models is found which in one dimension gives self-affine interfaces with roughness exponent χ, which is seen that roughness can occur with higher exponents than in situations where global equilibration of the driving force is not established.

Limiting forms of the frequency distribution of the largest or smallest member of a sample

- Mathematics, Geology
- 1928

The limiting distribution, when n is large, of the greatest or least of a sample of n , must satisfy a functional equation which limits its form to one of two main types. Of these one has, apart from…