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Lévy Diffusion Under Power-Law Stochastic Resetting.

Jianli Liu1, Yunyun Li1, Fabio Marchesoni1,2

  • 1MOE Key Laboratory of Advanced Micro-Structured Materials, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China.

Entropy (Basel, Switzerland)
|January 28, 2026
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Summary
This summary is machine-generated.

Stochastic resetting of Lévy walks reveals distinct diffusive behaviors. Power-law resetting creates three regimes, including superdiffusion and localization, impacting search strategies.

Keywords:
Brownian motionLévy walkstochastic resetting

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Area of Science:

  • Statistical Physics
  • Complex Systems
  • Non-equilibrium Dynamics

Background:

  • Lévy walks exhibit anomalous diffusion, crucial for modeling phenomena from finance to biology.
  • Stochastic resetting introduces a mechanism to confine random processes, altering their long-term behavior.

Purpose of the Study:

  • To investigate the impact of different resetting strategies on Lévy walk diffusive dynamics.
  • To characterize the mean squared displacement (MSD) under exponential and power-law resetting protocols.

Main Methods:

  • Combined numerical simulations and theoretical analysis using renewal theory.
  • Derivation of mean squared displacement (MSD) scaling laws for various resetting exponents.

Main Results:

  • Exponential resetting leads to a sharp transition from superdiffusion to a saturated steady state.
  • Power-law resetting (exponent β) results in three distinct MSD regimes: free superdiffusion (β<1), tunable superdiffusion (1<β<γ0+1), and localization (β>γ0+1).
  • Theoretical MSD scaling laws show excellent agreement with simulation data.

Conclusions:

  • The study provides a comprehensive understanding of how stochastic resetting shapes Lévy walk diffusion.
  • Findings offer insights into optimizing search strategies and controlling transport in complex, non-equilibrium systems.