Graphon particle systems with common noise
Probability
2026-04-28 v3
Abstract
We study a nonlinear graphon particle system driven by both idiosyncratic and common noise, where interactions are governed by a graphon and represented as positive finite measures. Each particle evolves via a McKean-Vlasov-type SDE with graphon-weighted conditional laws. We prove a law of large numbers for the empirical and interaction measures, using generalized Wasserstein metrics and weak convergence techniques suited for the non-Markovian structure induced by common noise.
Cite
@article{arxiv.2507.03265,
title = {Graphon particle systems with common noise},
author = {Erhan Bayraktar and Xihao He and Donghan Kim},
journal= {arXiv preprint arXiv:2507.03265},
year = {2026}
}
Comments
33 pages