Latent Voter Model on Locally Tree-Like Random Graphs

TL;DR

This paper analyzes the latent voter model on random graphs, showing that a small latent period leads to a long-lasting quasi-stationary state with balanced opinions, significantly altering traditional voter model dynamics.

Contribution

It introduces and studies the latent voter model on random graphs, demonstrating the emergence of a long-lived quasi-stationary state due to the latent period.

Findings

Presence of a quasi-stationary state with balanced opinions

Persistence time of the state can be arbitrarily large as n increases

Small latent period drastically changes voter model behavior

Abstract

In the latent voter model, which models the spread of a technology through a social network, individuals who have just changed their choice have a latent period, which is exponential with rate $\lambda$, during which they will not buy a new device. We study site and edge versions of this model on random graphs generated by a configuration model in which the degrees $d(x)$ have $3 \le d(x) \le M$. We show that if the number of vertices $n \to\infty$ and $\log n \ll \lambda_n \ll n$ then the latent voter model has a quasi-stationary state in which each opinion has probability $\approx 1/2$ and persists in this state for a time that is $\ge n^m$ for any $m<\infty$. Thus, even a very small latent period drastically changes the behavior of the voter model.