English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

New quantitative propagation of chaos results for mean field diffusion areproved via local and global entropy estimates. In the first result we work onthe torus and consider singular, divergence free interactions $K\in L^p$,$p>d$. We prove a $O(k^{2}/n^2)$ convergence rate in relative entropy betweenthe $k$-marginal laws of the particle system and its limiting law at each time$t$, as long as the same holds at time 0. The proof is based on local estimatesvia a form of BBGKY hierarchy and exemplifies a method to extend the frameworkin Lacker [16] to singular interactions. The rate can be made uniform in timecombined with the result in [18]. Then we prove quantitative propagation ofchaos for interactions that are only assumed to have linear growth. Thisgeneralizes to the case where the driving noise is replaced by a fractionalBrownian motion $B^H$, for all $H\in(0,1)$. These proofs follow from globalestimates and subGaussian concentration inequalities. We obtain $O(k/n)$convergence rate in relative entropy in each case, yet the rate is only validon $[0,T^*]$ with $T^*$ a fixed finite constant depending on various parametersof the system.

Entropic propagation of chaos for mean field diffusion with $L^p$ interactions via hierarchy, linear growth and fractional noise