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We prove the optimal rate of quantitative propagation of chaos, uniformly in time, for interacting diffusions.
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V.I. Bogachev, M. Röckner, and S.V. Shaposhnikov, Distances between transition probabilities of diffusions and applications to nonlinear Fokker–Planck–Kolmogorov equations , Journal of Functional Analysis 271
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A. Durmus, A. Eberle, A. Guillin, and R. Zimmer, An elementary approach to uniform in time propagation of chaos , Proc. Amer. Math. Soc. 148
2020
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by same author, A gradient flow approach of propagation of chaos , Discrete & Continuous Dynamical Systems 40
2020
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J. Sirignano and K. Spiliopoulos, Mean field analysis of neural networks: A law of large numbers , SIAM Journal on Applied Mathematics 80
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2021
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F. Delarue and A. Tse, Uniform in time weak propagation of chaos on the torus , arXiv (2021)
2021
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F. Golse, On the dynamics of large particle systems in the mean field limit , Macroscopic and large scale phenomena: coarse graining, mean field limits and ergodicity, Springer, 2016, pp. 1–144
2016
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P.-E. Jabin and Z. Wang, Mean field limit and propagation of chaos for Vlasov systems with bounded forces , Journal of Functional Analysis 271
2016
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by same author, Mean field limit for stochastic particle systems , Active Particles, Volume 1, Springer, 2017, pp. 379–402
2017
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L. Chizat and F. Bach, On the global convergence of gradient descent for over-parameterized models using optimal transport , Proceedings of the 32nd International Conference on Neural Information Processing Systems (2018), 3040–3050
2018
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by same author, Quantitative estimates of propagation of chaos for stochastic systems with W − 1 , ∞ {W}^{-1,\infty} kernels , Inventiones mathematicae 214
2018
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S. Mei, A. Montanari, and P.-M. Nguyen, A mean field view of the landscape of two-layer neural networks , Proceedings of the National Academy of Sciences of the United States of America 115
2018
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2018
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2021
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2021
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A. Guillin and P.Monmarche, Uniform long-time and propagation of chaos estimates for mean field kinetic particles in non-convex landscapes , Journal of Statistical Physics 185
2021
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2021
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2021
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D. Lacker, Hierarchies, entropy, and quantitative propagation of chaos for mean field diffusions , Preprint (2021)
2021
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by same author, Quantitative approximate independence for continuous mean field gibbs measures , Preprint (2021)
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