Evergreen Ballroom H

### Withdrawn - Opinion Dynamics with Confidence Threshold (306524)

**Mela Hardin, Arizona State University*

**Keywords:** voter model, opinion dynamics

Interacting particle systems is a field of probability theory devoted to the rigorous analysis of certain types of models that arise in other fields such as physics, biology, and economics. One popular example of such systems is the voter model for the dynamics of opinions. The general opinion model in this talk is a variant of the voter model. We use two connected graphs, one representing the set of opinions, the other the set of individuals with those opinions as their respective set of vertices. Pairs of neighbors in the spatial graph interact at rate one unless the geodesic distance between their opinions exceeds some confidence threshold. Each interaction results in the opinion of one of the two individuals moving one step towards the opinion of the other individual. The main question about the general opinion model on infinite graphs is whether the system fluctuates and clusters, leading to a global consensus, or fixates in a fragmented configuration. When the underlying spatial structure is a finite connected graph, the process fixates after an almost surely finite time, and we study lower bounds for the probability that, at this time, the system reaches consensus.