Uniform in time propagation of chaos for noisy mean-field coupled maps

@misc{tenaglia2026uniform,
  title = {{Uniform in time propagation of chaos for noisy mean-field coupled maps}},
  author = {Giuseppe Tenaglia and Matteo Tanzi},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.05769},
  eprint = {2609.05769},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.05769},
}

TY  - UNPB
TI  - Uniform in time propagation of chaos for noisy mean-field coupled maps
AU  - Giuseppe Tenaglia
AU  - Matteo Tanzi
PY  - 2026
DA  - 2026/09/04
PB  - arXiv
DO  - 10.48550/arxiv.2609.05769
UR  - https://arxiv.org/abs/2609.05769
AB  - We study discrete-time N-dimensional mean-field systems on the torus subject to additive noise whose probability density is bounded away from zero. Given a Lipschitz one-particle map and interaction term, we prove that, if the lower bound on the noise density is sufficiently large, the N-dimensional transfer operator 𝒫_N preserves a dimension-independent class of sub-Gaussian probability measures. Moreover, 𝒫_N is a one-step contraction in the Dobrushin-Wasserstein distance and therefore admits a unique invariant measure ρ_N, which is itself sub-Gaussian. Under the same condition on the noise strength, we show that the associated self-consistent transfer operator is a one-step contraction in Wasserstein distance and hence admits a unique fixed point ρ. We further prove, using these contraction estimates, that 𝒫_N preserves an O(N^−1/2) neighbourhood of the product measure ρ^⊗ N in the Dobrushin-Wasserstein metric, and in particular that ρ_N belongs to this neighbourhood. Finally, we establish uniform-in-time propagation of chaos in the Dobrushin-Wasserstein metric and, under the additional assumption that the noise density is of bounded variation, in total variation for every fixed-dimensional marginal.
ER  -