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Anomalous persistence exponents for normal yet aging diffusion.

A Barbier-Chebbah1, O Benichou1, R Voituriez2

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This summary is machine-generated.

This study reveals anomalous persistence exponents in ageing processes, even with normal diffusion. The findings suggest a new criterion for identifying anomalous exponents in fluctuating systems.

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Area of Science:

  • Statistical Physics
  • Stochastic Processes

Background:

  • The persistence exponent (θ) quantifies long-time decay in stochastic processes, crucial for fluctuating systems.
  • Anomalous exponents (θ≠1/2) were previously linked only to anomalous diffusion (H≠1/2).

Purpose of the Study:

  • To identify anomalous persistence exponents in processes exhibiting normal diffusive scaling (H=1/2).
  • To analytically determine these anomalous exponents and propose a general criterion.

Main Methods:

  • Analytical determination of persistence exponents.
  • Analysis of ageing processes with normal diffusive scaling.

Main Results:

  • Demonstration of anomalous persistence exponents (θ≠1/2) in asymptotically diffusive processes (H=1/2).
  • Identification of ageing and time-dependent increments as key factors for anomalous exponents.

Conclusions:

  • A new criterion is proposed: anomalous persistence exponents occur in diffusive processes if increments exhibit ageing and time-dependence across all scales.
  • This expands the understanding of persistence phenomena beyond anomalous diffusion.