Roughness scaling for Edwards-Wilkinson relaxation in small-world networks
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Updated: Aug 24, 2026

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
Published on: December 7, 2021
B Kozma1, M B Hastings, G Korniss
1Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180-3590, USA. kozmab@rpi.edu
Abstract:
Motivated by a fundamental synchronization problem in scalable parallel computing and by a recent criterion for "mean-field" synchronizability in interacting systems, we study the Edwards-Wilkinson model on two variations of a small-world network. In the first version each site has exactly one random link of strength p, while in the second one each site on average has p links of unit strength. We construct a perturbative description for the width of the stationary-state surface (a measure of synchronization), in the weak- and sparse-coupling limits, respectively, and verify the results by performing exact numerical diagonalization. The width remains finite in the limit of infinite system size for both cases, but exhibits anomalous scaling with p in the latter for d< or =2.
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