Vlasov equations on directed hypergraph measures

Christian Kuehn () and Chuang Xu ()
Additional contact information
Christian Kuehn: Technical University of Munich
Chuang Xu: University of Hawai’i at Mānoa

Partial Differential Equations and Applications, 2025, vol. 6, issue 1, 1-49

Abstract: Abstract In this paper we propose a framework to investigate the mean field limit (MFL) of interacting particle systems on directed hypergraphs. We provide a non-trivial measure-theoretic viewpoint and make extensions of directed hypergraphs as directed hypergraph measures (DHGMs), which are measure-valued functions on a compact metric space. These DHGMs can be regarded as hypergraph limits which include limits of a sequence of hypergraphs that are sparse, dense, or of intermediate densities. Our main results show that the Vlasov equation on DHGMs are well-posed and its solution can be approximated by empirical distributions of large networks of higher-order interactions. The results are applied to a Kuramoto network in physics, an epidemic network, and an ecological network, all of which include higher-order interactions. To prove the main results on the approximation and well-posedness of the Vlasov equation on DHGMs, we robustly generalize the method of [Kuehn, Xu. Vlasov equations on digraph measures, JDE, 339 (2022), 261–349] to higher-dimensions.

Keywords: Mean field limit; Higher-order interaction; Hypergraphs; Kuramoto model; Epidemic dynamics; Lotka–Volterra systems; Sparse networks; 35R02; 35Q84; 05C65 (search for similar items in EconPapers)
Date: 2025
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s42985-025-00313-6 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:pardea:v:6:y:2025:i:1:d:10.1007_s42985-025-00313-6

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/42985/

DOI: 10.1007/s42985-025-00313-6

Access Statistics for this article

Partial Differential Equations and Applications is currently edited by Zhitao Zhang

More articles in Partial Differential Equations and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().