Quasi-Stationary Distributions for the Voter Model on Complete Bipartite Graph
In this talk I will discuss the discrete-time voter model for opinion dynamics and its quasistationary distribution (QSD). The focus will be on the sequence of QSDs corresponding to the model on complete bipartite graphs with a "large" partition whose size tends to infinity and a "small" partition of constant size. In this case, the QSDs converge to a nontrivial limit featuring a consensus, except for a random number of dissenting vertices in the large partition which follows the heavy-tailed Sibuya distribution. The results rely on duality between the voter model and coalescing random walks through time-reversal. Time permitting, I'll expand the discussion on the duality and its application to a broader class of processes. The research presented in this talk was carried out during the 2019 UConn Markov Chains REU and is joint work with Hugo Panzo and student participants Philip Speegle and R. Oliver VandenBerg. arXiv:2004.10187.