Coupling and Tensorization of Kinetic Theory and Graph Theory
Abstract
We study a non-exchangeable multi-agent system and rigorously derive a strong form of the mean-field limit. The convergence of the connection weights and the initial data implies convergence of large-scale dynamics toward a deterministic limit given by the corresponding extended Vlasov PDE, at any later time and any realization of randomness. This is established on what we call a bi-coupling distance defined through a convex optimization problem, which is an interpolation of the optimal transport between measures and the fractional overlay between graphs. The proof relies on a quantitative stability estimate of the so-called observables, which are tensorizations of agent laws and graph homomorphism densities. This reveals a profound relationship between mean-field theory and graph limiting theory, intersecting in the study of non-exchangeable systems.
Cite
@article{arxiv.2412.14512,
title = {Coupling and Tensorization of Kinetic Theory and Graph Theory},
author = {Datong Zhou},
journal= {arXiv preprint arXiv:2412.14512},
year = {2025}
}