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Quantitative propagation of chaos for particle systems with memory and their long-time behaviour

  • Adrienne Le Meur
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Abstract

We study a class of interacting diffusion particle systems with memory and their mean-field limit using coupling methods. We first establish quantitative propagation of chaos estimates for this class of models. Our first main result is a uniform-in-time propagation of chaos estimate, under a suitable contraction condition. We also discuss conditions for existence of stationary solutions and show that long-time convergence to a non-stationary measure may also hold. This requires an asymptotic behaviour for the memory interaction and a memory loss condition. As a consequence, our second main result is that the particle system converges asymptotically to the same equilibrium up to the propagation of chaos error, which shows that the large-particle limit and the large-time limit are exchangeable.

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Cite

BibTeXRIS
BibTeX
@misc{meur2026quantitative,
  title = {{Quantitative propagation of chaos for particle systems with memory and their long-time behaviour}},
  author = {Adrienne Le Meur},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.10599},
  eprint = {2609.10599},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.10599},
}
RIS
TY  - UNPB
TI  - Quantitative propagation of chaos for particle systems with memory and their long-time behaviour
AU  - Adrienne Le Meur
PY  - 2026
DA  - 2026/09/07
PB  - arXiv
DO  - 10.48550/arxiv.2609.10599
UR  - https://arxiv.org/abs/2609.10599
AB  - We study a class of interacting diffusion particle systems with memory and their mean-field limit using coupling methods. We first establish quantitative propagation of chaos estimates for this class of models. Our first main result is a uniform-in-time propagation of chaos estimate, under a suitable contraction condition. We also discuss conditions for existence of stationary solutions and show that long-time convergence to a non-stationary measure may also hold. This requires an asymptotic behaviour for the memory interaction and a memory loss condition. As a consequence, our second main result is that the particle system converges asymptotically to the same equilibrium up to the propagation of chaos error, which shows that the large-particle limit and the large-time limit are exchangeable.
ER  -