Latent Voter Model

Latent Voter Model on Locally Tree-Like Random Graphs

Ran Hou and Rick Durrett

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 ≤ d(x) ≤ M. We show that if the number of vertices n → ∞ and log n << λ_n << n then the fraction of 1's at time λ_n t converges to du/dt = c_p u(1-u)(1-2u). Using this we show that the latent voter model has a quasi-stationary state in which each opinion has probability ≈ 1/2 and persists in this state for a time that is ≥ n^m for any m <∞. Thus, even a very small latent period drastically changes the behavior of the voter model, which has a one parameter family of stationary distributions and reaches fixation in time O(n)..

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