Sharp uniform-in-time propagation of chaos

A note on uniform in time mean-field limit in graphs

“…Let us also mention the optimal coupling approach of Salem (2020) using a WJ inequality, which is also used in Del Moral and Tugaut (2019), which enables to recover the results in Durmus et al (2020). Thanks to an analysis of the relative entropy through the BBGKY hierarchy, building upon the work of Lacker (2023), a result of uniform in time propagation of chaos was obtained, with a sharp rate in N , in Lacker and Le Flem (2023). Finally, in the recent work of Delarue and Tse (2021), uniform in time weak propagation of chaos (i.e observable by observable) was shown on the torus via Lions derivative.…”

Well‐posedness of diffusion–aggregation equations with bounded kernels and their mean‐field approximations

“…A drawback of the modulated free energy approach is that it requires the existence of an entropy solution on the particle level (microscopic level), see [29, Proposition 4.2], which is nontrivial outside a setting on the torus. Further results on propagation of chaos were proven for general L p -interaction force kernels k for first-and second-order systems on the torus [32] and on the whole space R d [33][34][35]. For instance, [35] provides optimal bounds on the relative entropy of order (k 2 ∕N 2 ) by exploiting the BBGKY-hierarchy combined with delicate estimates on the error of iterations.…”

“…Further results on propagation of chaos were proven for general L p -interaction force kernels k for first-and second-order systems on the torus [32] and on the whole space R d [33][34][35]. For instance, [35] provides optimal bounds on the relative entropy of order (k 2 ∕N 2 ) by exploiting the BBGKY-hierarchy combined with delicate estimates on the error of iterations.…”