<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>1</mml:mn><mml:mi>/</mml:mi><mml:mi mathvariant="italic">f</mml:mi></mml:math>Noise and Extreme Value Statistics

Antal, Tibor; Droz, Michel; Györgyi, G.; Rácz, Zoltán

doi:10.1103/physrevlett.87.240601

Cited by 149 publications

(184 citation statements)

References 29 publications

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“…Indeed, the EVS of time records with long-term persistence of Gaussian distributed fluctuations with a < 1 converges to the Fisher-Tippett distribution [48]. The same asymptotic law also determines the distribution of maximum heights of periodic, Gaussian 1/f -noise [43,49], where the maximum is measured relative to the mean.…”

Section: Quantitiymentioning

confidence: 97%

Universal fluctuations and extreme statistics of avalanches near the depinning transition

et al. 2013

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We derive exact predictions for universal scaling exponents and scaling functions associated with the statistics of maximum velocities vm during avalanches described by the mean field theory of the interface depinning transition. In particular, we find a robust power-law regime in the statistics of maximum events that can explain the observed distribution of the peak amplitudes in acoustic emission experiments of crystal plasticity. Our results are expected to be broadly applicable to a broad range of systems in the mean-field interface depinning universality class, ranging from magnets to earthquakes.

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Section: Quantitiymentioning

confidence: 97%

Universal fluctuations and extreme statistics of avalanches near the depinning transition

et al. 2013

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“…In our attempts to expand the picture gallery, we have recently derived [1] the following result: The scaling function for the roughness-distribution of a Gaussian periodic 1/f noise signal is one of the extreme value distributions, the Fisher-Tippet-Gumbel distribution [27,28]. This is a rather unexpected and interesting result and we feel that it is important to explore its generality and limitations.…”

Section: Introductionmentioning

confidence: 99%

Roughness distributions for1/fαsignals

et al. 2002

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The probability density function (PDF) of the roughness, i.e., of the temporal variance, of 1/f α noise signals is studied. Our starting point is the generalization of the model of Gaussian, timeperiodic, 1/f noise, discussed in our recent Letter [1], to arbitrary power law. We investigate three main scaling regions (α ≤ 1/2, 1/2 < α ≤ 1, and 1 < α), distinguished by the scaling of the cumulants in terms of the microscopic scale and the total length of the period. Various analytical representations of the PDF allow for a precise numerical evaluation of the scaling function of the PDF for any α. A simulation of the periodic process makes it possible to study also non-periodic, thus experimentally more relevant, signals on relatively short intervals embedded in the full period. We find that for α ≤ 1/2 the scaled PDF-s in both the periodic and the non-periodic cases are Gaussian, but for α > 1/2 they differ from the Gaussian and from each other. Both deviations increase with growing α. That conclusion, based on numerics, is reinforced by analytic results for α = 2 and α → ∞, in the latter limit the scaling function of the PDF being finite for periodic signals, but developing a singularity for the aperiodic ones. Finally, an overview is given for the scaling of cumulants of the roughness and the various scaling regions in arbitrary dimensions. We suggest that our theoretical and numerical results open a new perspective on the data analysis of 1/f α processes.

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“…It appears in the analysis of wide variety of physical systems as discussed e.g. in [24]. We depict it in figure 1.…”

Section: Dsmentioning

confidence: 99%

“…distributions of maxima or minima of a set of random variables. They pop up in a wild variety of physical systems (see for example [24]). Interestingly, the same Gumbel distribution was found very recently in [25] as the distance distribution for a free massless scalar in dS 2 , but for an a priori rather different distance measure, suggesting it is a universal feature.…”

Section: Jhep06(2016)181mentioning

confidence: 99%

Cosmic clustering

Anninos

Denef

2016

J. High Energ. Phys.

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We show that the late time Hartle-Hawking wave function for a free massless scalar in a fixed de Sitter background encodes a sharp ultrametric structure for the standard Euclidean distance on the space of field configurations. This implies a hierarchical, tree-like organization of the state space, reflecting its genesis as a branched diffusion process. An equivalent mathematical structure organizes the state space of the Sherrington-Kirkpatrick model of a spin glass.

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1/fNoise and Extreme Value Statistics

Cited by 149 publications

References 29 publications

Universal fluctuations and extreme statistics of avalanches near the depinning transition

Universal fluctuations and extreme statistics of avalanches near the depinning transition

Roughness distributions for1/fαsignals

Cosmic clustering

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