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Deviations from Gaussianity in deterministic discrete time dynamical systems.

Jeroen Wouters1

  • 1Department of Mathematics and Statistics, University of Reading, Reading RG6 6AX, United Kingdom.

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Summary
This summary is machine-generated.

This study explores deviations from normal distribution for random variables. Edgeworth expansions offer a universal method to describe these deviations, with accurate numerical evidence provided.

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Area of Science:

  • Statistical physics
  • Probability theory
  • Dynamical systems

Background:

  • Understanding deviations from the normal distribution is crucial in statistical analysis.
  • Deterministic maps can generate complex random variable behavior.
  • Asymptotic expansions are key tools for approximating probability distributions.

Purpose of the Study:

  • To investigate deviations from Gaussianity in specific random variable types.
  • To demonstrate the utility of Edgeworth expansions in characterizing these deviations.
  • To derive and validate explicit formulas for asymptotic expansions.

Main Methods:

  • Analysis of random variables generated by deterministic discrete time maps.
  • Examination of linearly damped variables driven by deterministic maps.
  • Application and derivation of Edgeworth expansion formulas.

Main Results:

  • Edgeworth expansions provide a universal description of deviations from normality.
  • Explicit expressions for asymptotic expansions were successfully derived.
  • Numerical simulations confirmed the accuracy of the derived expansions.

Conclusions:

  • The findings offer a generalized framework for understanding deviations from Gaussian behavior.
  • Edgeworth expansions are effective for quantifying deviations in the studied systems.
  • The study validates the theoretical predictions with empirical numerical evidence.