Consensus and discordance in the Axelrod model for the dynamics of cultures

The Axelrod model is a spatial stochastic model for the dynamics of cultures which includes two key social components: homophily, the tendency of individuals to interact more frequently with individuals who are more similar, and social influence, the tendency of individuals to become more similar when they interact. Each individual is characterized by a collection of opinions about different issues, and pairs of neighbors interact at a rate equal to the number of issues for which they agree, which results in the interacting pair agreeing on one more issue. This model has been extensively studied during the past 20 years based on numerical simulations and heuristic arguments while there is a lack of analytical results. This talk gives rigorous fluctuation and fixation results for the one-dimensional system that sometimes confirms and sometimes refutes some of the conjectures formulated by applied scientists.