Voter models on subcritical scale‐free random graphs. Issue 2 (23rd July 2022)

• Record Type: Journal Article
• Authors: Fernley, John; Ortgiese, Marcel
• Is Part Of: Random structures & algorithms. Volume 62:Issue 2(2023)
• Page Start: 376
• Page End: 429
• Publication Date: 2022-07-23
• Subjects: inhomogeneous random graphs -- interacting particle systems -- random walks on random graphs -- scale‐free networks -- voter model; Random graphs -- Periodicals; Mathematical analysis -- Periodicals; 519
• DOI: 10.1002/rsa.21107
• Languages: English
• ISSNs: 1042-9832

Abstract

Abstract: The voter model is a classical interacting particle system modelling how consensus is formed across a network. We analyze the time to consensus for the voter model when the underlying graph is a subcritical scale‐free random graph. Moreover, we generalize the model to include a "temperature" parameter controlling how the graph influences the speed of opinion change. The interplay between the temperature and the structure of the random graph leads to a very rich phase diagram, where in the different phases different parts of the underlying geometry dominate the time to consensus. Finally, we also consider a discursive voter model, where voters discuss their opinions with their neighbors. Our proofs rely on the well‐known duality to coalescing random walks and a detailed understanding of the structure of the random graphs.