Voter models on subcritical inhomogeneous random graphs

John Fernley; Marcel Ortgiese

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arXiv · 1911.13187

Voter models on subcritical inhomogeneous random graphs

John Fernley·Marcel Ortgiese

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Abstract

The voter model is a classical interacting particle system modelling how consensus is formed across a network. We analyse the time to consensus for the voter model when the underlying graph is a subcritical scale-free random graph. Moreover, we generalise the model to include a `temperature' parameter. 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 neighbours. Our proofs rely on the well-known duality to coalescing random walks and a detailed understanding of the structure of the random graphs.

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John Fernley, Marcel Ortgiese. 2020-06-01. Voter models on subcritical inhomogeneous random graphs. https://arxiv.org/abs/1911.13187

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