Local persistence exponent and its log-periodic oscillations
Statistical Mechanics
2025-07-14 v1 Chemical Physics
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.
Keywords
Cite
@article{arxiv.2507.08628,
title = {Local persistence exponent and its log-periodic oscillations},
author = {Yilin Ye and Denis S. Grebenkov},
journal= {arXiv preprint arXiv:2507.08628},
year = {2025}
}