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Area of Science:

  • Physics
  • Statistical Mechanics
  • Stochastic Processes

Background:

  • Continuous-time random walks (CTRW) are fundamental models for anomalous diffusion.
  • Resetting mechanisms introduce non-equilibrium dynamics, altering particle behavior.
  • Scaled Brownian motion (SBM) serves as a mean-field approximation for CTRW.

Purpose of the Study:

  • To analyze the impact of power-law resetting on CTRW dynamics.
  • To investigate conditions for universal behavior in displacement probability density functions (PDF).
  • To compare CTRW behavior under different resetting schemes with SBM.

Main Methods:

  • Theoretical analysis of CTRW with power-law waiting and resetting times.
  • Calculation of mean-squared displacement (MSD).
  • Asymptotic analysis of probability density functions (PDFs).

Main Results:

  • The MSD of CTRW with resetting follows the same behavior as SBM.
  • Under complete resetting, CTRW PDFs exhibit universal behavior consistent with SBM.
  • Under incomplete resetting, CTRW PDFs diverge significantly from SBM behavior.

Conclusions:

  • Resetting significantly influences CTRW, leading to universal MSD behavior akin to SBM.
  • Complete resetting preserves SBM-like PDF universality, while incomplete resetting breaks it.
  • The study highlights the critical role of resetting type in determining stochastic process outcomes.