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Complete decomposition of anomalous diffusion in variable speed generalized Lévy walks
Abhijit Bera1, Kevin E Bassler2
1University of Houston, University of Houston, Department of Physics, USA and Texas Center for Superconductivity, USA.
Physical Review. E
|July 24, 2026
Summary
Variable speed generalized Lévy walks (VGLWs) unify diverse stochastic models. Anomalous diffusion in VGLWs arises from a combination of Joseph, Noah, and Moses effects, with an unbounded Noah exponent revealing extreme behaviors.
Area of Science:
- Statistical Physics
- Stochastic Processes
- Complex Systems
Background:
- Lévy walks are fundamental stochastic processes modeling anomalous diffusion.
- Existing models often focus on single mechanisms violating the Central Limit Theorem (CLT).
- A unified framework is needed to explore complex anomalous diffusion behaviors.
Purpose of the Study:
- Introduce and analyze Variable Speed Generalized Lévy Walks (VGLWs).
- Decompose anomalous diffusion in VGLWs into constitutive effects (Joseph, Noah, Moses).
- Investigate the range and nature of anomalous diffusion within the VGLW framework.
Main Methods:
- Mathematical modeling of spatiotemporally coupled stochastic processes.
- Decomposition of anomalous diffusion into three CLT-violating effects.
- Analysis of the unboundedness of the Noah exponent (L) in VGLWs.
Main Results:
- Anomalous diffusion in VGLWs typically results from a combination of Joseph, Noah, and Moses effects.
- The Noah exponent (L) in VGLWs is unbounded, indicating potentially more extreme diffusion than previously studied models.
- VGLWs offer a richer landscape for anomalous diffusion phenomena.
Conclusions:
- VGLWs provide a comprehensive framework for studying anomalous diffusion.
- The interplay of Joseph, Noah, and Moses effects is crucial for understanding VGLW dynamics.
- The unbounded Noah exponent highlights novel and extreme diffusive behaviors.
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