English

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.

Keywords

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

R2 v1 2026-07-01T03:46:11.178Z