Scaling limits for continuous opinion dynamics systems

Details Scaling limits for continuous opinion dynamics systems Scaling limits for continuous opinion dynamics systems

2010-03-17

arxiv.org/abs/1003.3384v3

Annals of Applied Probability 2011, Vol. 21, No. 4, 1537-1567

Mathematics

Probability

Published at http://dx.doi.org/10.1214/10-AAP739 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institu

Scientific paper

10.1214/10-AAP739

Scaling limits are analyzed for stochastic continuous opinion dynamics systems, also known as gossip models. In such models, agents update their vector-valued opinion to a convex combination (possibly agent- and opinion-dependent) of their current value and that of another observed agent. It is shown that, in the limit of large agent population size, the empirical opinion density concentrates, at an exponential probability rate, around the solution of a probability-measure-valued ordinary differential equation describing the system's mean-field dynamics. Properties of the associated initial value problem are studied. The asymptotic behavior of the solution is analyzed for bounded-confidence opinion dynamics, and in the presence of an heterogeneous influential environment.

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