Speaker: Siva Athreya
Venue: ICTS
Date: October 9, 2025

Interplay of vertex and edge dynamics for dense random graphs: The large population limits of opinion dynamics in homogeneous populations, on lattices and on general fixed graphs are quite well understood. We consider a process where the graph itself is dynamic and changes in response to the voter model process, thus creating interaction between the two. More precisely, we consider a dense random graph in which the vertices can hold opinion 0 or 1 and the edges can be closed or open. The vertices update their opinion at a rate proportional to the number of incident open edges, and do so by adopting the opinion of the vertex at the other end. The edges update their status at a constant rate, and do so by switching between closed and open with a probability that depends on their status and on whether the vertices at their ends are concordant or discordant. We understand the large n limit of this co-evolution and describe the limiting evolution. This is joint work with Frank den Hollander and Adrian Roellin.