Local persistence exponent and its log-periodic oscillations

Yilin Ye; Denis S. Grebenkov

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arXiv · 2507.08628

Local persistence exponent and its log-periodic oscillations

Yilin Ye·Denis S. Grebenkov

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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.

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Yilin Ye, Denis S. Grebenkov. 2025-07-11. Local persistence exponent and its log-periodic oscillations. https://arxiv.org/abs/2507.08628

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