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Modeling and statistical analysis of non-gaussian random fields with heavy-tailed distributions

Ghasemi Nezhadhaghighi, M ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.1103/PhysRevE.95.042114
  3. Abstract:
  4. In this paper, we investigate and develop an alternative approach to the numerical analysis and characterization of random fluctuations with the heavy-tailed probability distribution function (PDF), such as turbulent heat flow and solar flare fluctuations. We identify the heavy-tailed random fluctuations based on the scaling properties of the tail exponent of the PDF, power-law growth of qth order correlation function, and the self-similar properties of the contour lines in two-dimensional random fields. Moreover, this work leads to a substitution for the fractional Edwards-Wilkinson (EW) equation that works in the presence of μ-stable Lévy noise. Our proposed model explains the configuration dynamics of the systems with heavy-tailed correlated random fluctuations. We also present an alternative solution to the fractional EW equation in the presence of μ-stable Lévy noise in the steady state, which is implemented numerically, using the μ-stable fractional Lévy motion. Based on the analysis of the self-similar properties of contour loops, we numerically show that the scaling properties of contour loop ensembles can qualitatively and quantitatively distinguish non-Gaussian random fields from Gaussian random fluctuations. © 2017 American Physical Society
  5. Keywords:
  6. Distribution functions ; Gaussian noise (electronic) ; Probability density function ; Probability distributions ; Alternative solutions ; Analysis and characterization ; Correlation function ; Heavy-tailed distribution ; Non-gaussian randoms ; Random fluctuation ; Scaling properties ; Self similar properties ; Gaussian distribution
  7. Source: Physical Review E ; Volume 95, Issue 4 , 2017 ; 24700045 (ISSN)
  8. URL: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.95.042114