CM2LA Seminar 2024

Title : On the convergence of nonlinear averaging dynamics with three-body interactions on hypergraphs

Speaker : Dr. Jinyeop Lee (Ludwig Maximilian University of Munich)

Abstract : In the talk, we study the convergence properties of discrete-time dynamics on 3-uniform hypergraphs. Using hypergraphs, we model multi-body interactions. TIn such systems, nodes update their states through a nonlinear averaging mechanism, influenced by the states of two neighboring nodes connected by a hyperedge. Contrary to the expected behavior in linear dynamics on graphs, our findings show that the system does not simply converge to the average of the initial states. Unlike linear averaging dynamics on graphs with two-body interactions, this model does not converge to the average of the initial states but rather induces a shift. By assuming random initial states and by making some regularity and density assumptions on the hypergraph, we prove that the dynamics converge to a multiplicatively-shifted average of the initial states with high probability. This research was conducted in collaboration with E. Cruciani and E. L. Giacomelli.