# Mean Field Limits of Heterogeneous Networks

### Chuang Xu – University of Hawaiʻi at Mānoa, United States

Many science phenomena are described as interacting particle systems (IPS). The mean field limit (MFL) of large all-to-all coupled deterministic IPS is given by the solution of a PDE, the Vlasov Equation. Yet, many applications demand IPS coupled on networks/graphs, which are mostly heterogeneous. It is interesting to know, how the limit of a sequence of digraphs associated with the IPS influences the macroscopic MFL. In this talk, I will briefly introduce our recent work on Vlasov equations on a generalized digraph, regarded as the limit of a sequence of digraphs, which we refer to as a digraph measure (DGM).Such DGM is a natural extension of graphon, the limit of a sequence of dense graphs. It is noteworthy that DGM can be regarded as a limit of a sequence of digraphs of different densities (dense, sparse, or of intermediate densities). I will make some comparison between some recent results on MFL of IPS on graph limits and our contribution. Finally, I will talk about some applications of our results. This is a joint work with Prof. Christian Kuehn at the Technical University of Munich.

Biography: Chuang Xu is an assistant professor in the Department of Mathematics at the University of Hawaiʻi at Mānoa (UHM). Before joining UHM, he was an Alexander von Humboldt postdoc fellow and Technical University Foundation Fellow (TUFF) at the Technical University of Munich. Before that, he was a postdoc in the MBIO group at the University of Copenhagen. He received his PhD in Applied Mathematics from the University of Alberta in 2018. His research interests are (1) approximation of measures, (2) chemical reaction network theory, (3) mean field theory of interacting particle systems on networks.

### Location

Montréal Québec

Canada