Voter models on subcritical scale-free random graphs

John Fernley; Marcel Ortgiese

doi:10.1002/rsa.21107

Voter models on subcritical scale-free 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 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 language	English
Pages (from-to)	376-429
Number of pages	59
Journal	Random Structures and Algorithms
Volume	62
Issue number	2
Early online date	23 Jul 2022
DOIs	https://doi.org/10.1002/rsa.21107
Publication status	Published - 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.

Funding

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.

Keywords

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

Access to Document

10.1002/rsa.21107Licence: CC BY

voter_model_on_subcrit_IRGSubmitted manuscript, 2.77 MB

Cite this

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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.",

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Voter models on subcritical scale-free random graphs

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

Access to Document

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