Mean-field and fluctuations for hub dynamics in heterogeneous random networks
File(s)
Published version
Author(s)
Bian, Zheng
Lamb, Jeroen SW
Pereira, Tiago
Type
Journal Article
Abstract
We study a class of heterogeneous random networks, where the network degree distribution follows a power-law, and each node dynamics is a random dynamical system, interacting with neighboring nodes via a random coupling function. We characterize the hub behavior by the mean-field, subject to statistically controlled fluctuations. In particular, we prove that the fluctuations are small over exponentially long time scales and obtain Berry-Esseen estimates for the fluctuation statistics at any fixed time. Our results provide an explanation for several numerical observations, namely, a scaling relation between system size and frequency of large fluctuations, the system size induced desynchronization, and the Gaussian behavior of the fluctuations.
Date Issued
2025-07-01
Date Acceptance
2025-04-28
Citation
Communications in Mathematical Physics, 2025, 406 (7)
ISSN
0010-3616
Publisher
Springer
Journal / Book Title
Communications in Mathematical Physics
Volume
406
Issue
7
Copyright Statement
© The Author(s) 2025 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
License URL
Identifier
https://www.ncbi.nlm.nih.gov/pubmed/40568181
PII: 5335
Publication Status
Published
Coverage Spatial
Germany
Article Number
170
Date Publish Online
2025-06-23