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 | |
| 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.
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