Latent voter model on locally tree-like random graphs

In the latent voter model, individuals who have just changed their choice have a latent period, which is exponential with rate λ, during which they will not change their opinion. We study this model on random graphs generated by a configuration model with degrees 3≤d(x)≤M. We show that if the number of vertices n→∞ and logn≪λn≪n then there is a quasi-stationary state in which each opinion has probability ≈1∕2 and persists in this state for a time that is ≥nm for any m<∞.