Mean-field and Fluctuations for Hub Dynamics in Heterogeneous Random Networks
Zheng Bian, Jeroen S. W. Lamb, Tiago Pereira
TL;DR
This paper analyzes how hubs behave in large, randomly connected networks with power-law degree distributions.
Contribution
The paper provides a theoretical characterization of hub dynamics with statistically controlled fluctuations and proves fluctuation bounds over long time scales.
Findings
Fluctuations in hub dynamics remain small over exponentially long time scales.
The paper derives Berry-Esseen estimates for fluctuation statistics at fixed times.
Results explain numerical observations like Gaussian fluctuations and system size-induced desynchronization.
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.
Click any figure to enlarge with its caption.
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsOpinion Dynamics and Social Influence