Interplay of vertex and edge dynamics for dense random graph

Monday, October 28, 2024, 11:00 -- 11:30

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 rate $\eta$ times 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 rate $\rho$, 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 $n \rightarrow \infty$ limit of this co-evolution and describe the limiting evolution.

This is joint work with Frank den Hollander and Adrian Roellin.