Local persistence exponent and its log-periodic oscillations

2025/07/11 by Ye, Yilin, Grebenkov, Denis S.
#Chemical Physics (physics.chem-ph) #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech)

paper · doi:10.48550/arxiv.2507.08628

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.

Citations

• Boundary local time on wedges and prefractal curves
• First-passage times to a fractal boundary: local persistence exponent and its log-periodic oscillations
• Persistence and first-passage properties in nonequilibrium systems
• Random walks and Brownian motion: A method of computation for first-passage times and related quantities in confined geometries
• Narrow Escape, Part I

Related

• First-passage times to a fractal boundary: local persistence exponent and its log-periodic oscillations
• Scaling and Fractal formation in Persistence
• Persistence exponents of self-interacting random walks
• Persistence probabilities of a smooth self-similar anomalous diffusion process
• Persistence exponent for discrete-time, time-reversible processes