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This study explains the linearization effect in multifractal systems using Gaussian multiplicative chaos. Monte Carlo simulations confirm that Liouville-like random measures accurately model this phenomenon, preserving statistical properties.

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Area of Science:

  • Statistical Physics
  • Complex Systems
  • Turbulence Theory

Background:

  • Multifractal systems exhibit singularity spectra on bounded Hölder exponent sets.
  • Linearization effect: multifractal scaling exponents depend linearly on high statistical moment orders.
  • Turbulent intermittency models inspire the investigation of this effect.

Purpose of the Study:

  • Investigate the linearization effect in two-dimensional systems within Gaussian multiplicative chaos.
  • Explore the role of Liouville-like random measures in explaining the linearization effect.
  • Analyze the preservation of coarse-grained statistical properties in the linear regime.

Main Methods:

  • Monte Carlo simulations to verify theoretical predictions.
  • Framework of Gaussian multiplicative chaos (GMC).
  • Analysis of Liouville-like random measures with upper-bounded scalar fields.

Main Results:

  • The linearization effect in multifractal systems can be explained by Liouville-like random measures.
  • Gaussian multiplicative chaos properties are preserved in the linear scaling exponent regime.
  • Accurate evaluation of turbulent circulation statistical moments achieved.

Conclusions:

  • Liouville-like random measures provide a robust model for the linearization effect in multifractal systems.
  • Gaussian multiplicative chaos framework successfully describes observed phenomena.
  • The findings offer insights into turbulent circulation statistics.