Uniform-in-time propagation of chaos for second order interacting particle systems

Fuente: arXiv
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Hauptverfasser: Gong, Yun, Wang, Zhenfu, Xie, Pengzhi
Format: Preprint
Veröffentlicht: 2024
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author Gong, Yun
Wang, Zhenfu
Xie, Pengzhi
author_facet Gong, Yun
Wang, Zhenfu
Xie, Pengzhi
contents We study the long time behavior of second order particle systems interacting through global Lipschitz kernels. Combining hypocoercivity method in [37] and relative entropy method in [25], we are able to overcome the degeneracy of diffusion in position direction by controlling the relative entropy and relative Fisher information together. This implies the uniform-in-time propagation of chaos through the strong convergence of all marginals. Our method works at the level of Liouville equation and relies on the log Sobolev inequality of equilibrium of Vlasov-Fokker-Planck equation.
format Preprint
id arxiv_https___arxiv_org_abs_2409_02435
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Uniform-in-time propagation of chaos for second order interacting particle systems
Gong, Yun
Wang, Zhenfu
Xie, Pengzhi
Analysis of PDEs
Probability
We study the long time behavior of second order particle systems interacting through global Lipschitz kernels. Combining hypocoercivity method in [37] and relative entropy method in [25], we are able to overcome the degeneracy of diffusion in position direction by controlling the relative entropy and relative Fisher information together. This implies the uniform-in-time propagation of chaos through the strong convergence of all marginals. Our method works at the level of Liouville equation and relies on the log Sobolev inequality of equilibrium of Vlasov-Fokker-Planck equation.
title Uniform-in-time propagation of chaos for second order interacting particle systems
topic Analysis of PDEs
Probability
url https://arxiv.org/abs/2409.02435