MEAN FIELD LIMIT AND PROPAGATION OF CHAOS FOR LINEAR-FORMATION MODEL

  • Juntao WU ,
  • Xiao WANG ,
  • Yicheng LIU
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  • College of Sciences, National University of Defense Technology, Changsha 410073, China
Juntao Wu, E-mail: wu_jun_tao@163.com; Yicheng Liu, E-mail: liuyc2001@hotmail.com

Received date: 2024-03-04

  Revised date: 2025-02-20

  Online published: 2025-10-14

Supported by

This research was supported by the Natural Science Foundation of Hunan Province (2022JJ30655), the National Natural Science Foundation of China (12371180) and the Training Program for Excellent Young Innovators of Changsha (kq2305046).

Abstract

In this paper, we investigate the propagation of chaos for solutions to the Liouville equation derived from the Linear-Formation particle model. By imposing certain conditions, we derive the rate of convergence between the $k$-tensor product $f_{t}^{\otimes k}$ of the solution to be Linear-Formation kinetic equation and the $k$-marginal $f_{N,k}^{t}$ of the solution to the Liouville equation corresponding to the Linear-Formation particle model. Specifically, the following estimate holds in terms of $p$-Wasserstein ($1 \leqslant p <\infty$) distance $$ W^p_p(f_{t}^{\otimes k},f_{N,k}^{t}) \leqslant C_{1} \frac{k}{N^{\min(p/2,1)}}\left(1+t^{p}\right){\rm e}^{C_{2}t}, \quad 1\leqslant k\leqslant N. $$

Cite this article

Juntao WU , Xiao WANG , Yicheng LIU . MEAN FIELD LIMIT AND PROPAGATION OF CHAOS FOR LINEAR-FORMATION MODEL[J]. Acta mathematica scientia, Series B, 2025 , 45(5) : 2217 -2250 . DOI: 10.1007/s10473-025-0522-y

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