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1/f Noise and Extreme Value Statistics

T. Antal·M. Droz·G. Gyorgyi·Z. Racz
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Abstract

We study the finite-size scaling of the roughness of signals in systems displaying Gaussian 1/f power spectra. It is found that one of the extreme value distributions (Gumbel distribution) emerges as the scaling function when the boundary conditions are periodic. We provide a realistic example of periodic 1/f noise, and demonstrate by simulations that the Gumbel distribution is a good approximation for the case of nonperiodic boundary conditions as well. Experiments on voltage fluctuations in GaAs films are analyzed and excellent agreement is found with the theory.

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T. Antal, M. Droz, G. Gyorgyi, Z. Racz. 2001-05-30. 1/f Noise and Extreme Value Statistics. https://doi.org/10.1103/physrevlett.87.240601

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