Voter models on subcritical scale-free random graphs

John Fernley, Marcel Ortgiese

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2 Citations (SciVal)
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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.

Original languageEnglish
Pages (from-to)376-429
Number of pages59
JournalRandom Structures and Algorithms
Issue number2
Early online date23 Jul 2022
Publication statusPublished - Mar 2023

Bibliographical note

Funding Information:
We would like to thank Peter Mörters and Alexandre Stauffer for many useful discussions. JF was supported by a scholarship from the EPSRC Centre for Doctoral Training in Statistical Applied Mathematics at Bath (SAMBa), under the project EP/L015684/1.


  • inhomogeneous random graphs
  • interacting particle systems
  • random walks on random graphs
  • scale-free networks
  • voter model

ASJC Scopus subject areas

  • Software
  • General Mathematics
  • Computer Graphics and Computer-Aided Design
  • Applied Mathematics


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