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Propagation of Chaos on Riemannian Manifolds

  • Myeongju Chae
  • Gunhee Cho
  • Hyun Chul Jang
  • Guang Yang
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Abstract

We extend reflection coupling for uniform-in-time propagation of chaos from Euclidean space to complete Riemannian manifolds. Intrinsic reflection along minimizing geodesics replaces the Euclidean difference process, and the associated endpoint-index term quantifies the competition between curvature, confinement, and interaction. Under an endpoint-index bound and a radial Laplacian bound, we establish global well-posedness, uniform moment estimates, and uniform-in-time propagation of chaos with rate N−1/2 in a modified Wasserstein distance. We further obtain exponential contraction of the nonlinear McKean--Vlasov semigroup, uniqueness of its invariant probability measure among probability measures with finite second moment, and exponential convergence to equilibrium. Although a Ricci lower bound is an important special case, our framework also includes a curvature-spike class with infMRic=−∞.

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Cite

BibTeXRIS
BibTeX
@misc{chae2026propagation,
  title = {{Propagation of Chaos on Riemannian Manifolds}},
  author = {Myeongju Chae and Gunhee Cho and Hyun Chul Jang and Guang Yang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.12948},
  eprint = {2609.12948},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.12948},
}
RIS
TY  - UNPB
TI  - Propagation of Chaos on Riemannian Manifolds
AU  - Myeongju Chae
AU  - Gunhee Cho
AU  - Hyun Chul Jang
AU  - Guang Yang
PY  - 2026
DA  - 2026/09/11
PB  - arXiv
DO  - 10.48550/arxiv.2609.12948
UR  - https://arxiv.org/abs/2609.12948
AB  - We extend reflection coupling for uniform-in-time propagation of chaos from Euclidean space to complete Riemannian manifolds. Intrinsic reflection along minimizing geodesics replaces the Euclidean difference process, and the associated endpoint-index term quantifies the competition between curvature, confinement, and interaction. Under an endpoint-index bound and a radial Laplacian bound, we establish global well-posedness, uniform moment estimates, and uniform-in-time propagation of chaos with rate N^−1/2 in a modified Wasserstein distance. We further obtain exponential contraction of the nonlinear McKean--Vlasov semigroup, uniqueness of its invariant probability measure among probability measures with finite second moment, and exponential convergence to equilibrium. Although a Ricci lower bound is an important special case, our framework also includes a curvature-spike class with inf_MRic=−∞.
ER  -