Local persistence exponent and its log-periodic oscillations

Yilin Ye; Denis S. Grebenkov

doi:10.1016/j.physa.2025.131047

Local persistence exponent and its log-periodic oscillations

Yilin Ye
, Denis S. Grebenkov

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	131047
Journal	Physica A: Statistical Mechanics and its Applications
Volume	680
DOIs	https://doi.org/10.1016/j.physa.2025.131047
Publication status	Published - 15 Dec 2025

Keywords

Diffusion-controlled reactions
First-passage time
Fractals
Persistence exponent
Self-similarity
Survival probability

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10.1016/j.physa.2025.131047

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title = "Local persistence exponent and its log-periodic oscillations",

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 = "Diffusion-controlled reactions, First-passage time, Fractals, Persistence exponent, Self-similarity, Survival probability",

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AU - Ye, Yilin

AU - Grebenkov, Denis S.

PY - 2025/12/15

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N2 - 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.

AB - 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.

KW - Diffusion-controlled reactions

KW - First-passage time

KW - Fractals

KW - Persistence exponent

KW - Self-similarity

KW - Survival probability

UR - https://www.scopus.com/pages/publications/105019077108

U2 - 10.1016/j.physa.2025.131047

DO - 10.1016/j.physa.2025.131047

M3 - Article

AN - SCOPUS:105019077108

SN - 0378-4371

VL - 680

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

M1 - 131047

ER -

Local persistence exponent and its log-periodic oscillations

Abstract

Keywords

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