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Local persistence exponent and its log-periodic oscillations

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  • Ye, Yilin
  • Grebenkov, Denis S.

Abstract

We investigate the local persistence exponent of the survival probability of a particle diffusing near an absorbing self-similar boundary. We show by extensive Monte Carlo simulations that the local persistence exponent exhibits log-periodic oscillations over a broad range of timescales. We determine the period and mean value of these oscillations in a family of Koch snowflakes of different fractal dimensions. The effect of the starting point and its local environment on this behavior is analyzed in depth by a simple yet intuitive model. This analysis uncovers how spatial self-similarity of the boundary affects the diffusive dynamics and its temporal characteristics in complex systems.

Suggested Citation

  • Ye, Yilin & Grebenkov, Denis S., 2025. "Local persistence exponent and its log-periodic oscillations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 680(C).
    • Handle: RePEc:eee:phsmap:v:680:y:2025:i:c:s0378437125006995
    DOI: 10.1016/j.physa.2025.131047
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    References listed on IDEAS

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    1. Luck, Jean-Marc, 2024. "Revisiting log-periodic oscillations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 643(C).
    2. T. Guérin & N. Levernier & O. Bénichou & R. Voituriez, 2016. "Mean first-passage times of non-Markovian random walkers in confinement," Nature, Nature, vol. 534(7607), pages 356-359, June.
    3. N. Levernier & M. Dolgushev & O. Bénichou & R. Voituriez & T. Guérin, 2019. "Survival probability of stochastic processes beyond persistence exponents," Nature Communications, Nature, vol. 10(1), pages 1-7, December.
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