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Related Experiment Videos

Outliers, extreme events, and multiscaling.

V S L'vov1, A Pomyalov, I Procaccia

  • 1Department of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100, Israel.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 21, 2001
PubMed
Summary

Extreme events in natural and manmade systems can be predicted by studying their dynamics. Analyzing extreme event onset and demise reveals characteristic scaling properties, enabling tail prediction for probability distributions.

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Area of Science:

  • Physics
  • Complex Systems
  • Statistical Mechanics

Background:

  • Extreme events play a significant role in natural phenomena (climate, earthquakes, turbulence) and manmade systems (financial markets).
  • Statistical analysis of systems with extreme events is challenging due to their outlier nature and dominance in probability distribution tails, leading to multiscaling behavior.
  • Understanding the dynamics of extreme events is crucial for accurate prediction and analysis.

Purpose of the Study:

  • To investigate the dynamics of the onset and demise of extreme events in complex systems.
  • To reveal characteristic dynamical scaling properties of extreme events distinct from the bulk fluctuations.
  • To demonstrate the utility of analyzing extreme event dynamics for predicting the functional form of probability distribution tails.

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Main Methods:

  • Employment of a shell model of turbulence to simulate and analyze extreme events.
  • Detailed examination of the dynamics governing the appearance and disappearance of extreme events.
  • Analysis of short-time horizons to identify outlier properties and scaling behaviors.

Main Results:

  • Extreme events exhibit dynamical scaling properties unique to them, not shared by the majority of fluctuations.
  • Analysis of short-time horizons, where extreme events appear as outliers, successfully predicts the tails of probability distribution functions.
  • These predictions align with data collected over significantly longer time horizons.

Conclusions:

  • Extreme events, though appearing unpredictable in the short term, are consistent components of multiscaling statistics over longer time scales.
  • Studying the dynamics of extreme events provides valuable insights into their behavior and predictive power.
  • The findings suggest a unified approach to understanding and predicting extreme events across diverse complex systems.