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

doi:10.1007/s10473-025-0522-y

摘要/Abstract

摘要： 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 $$ W^p_p(f_{t}^{\otimes k},f_{N,k}^{t}) \leqslant C_{1} \frac{k}{N^{\min(p/2,1)}}\left(1+t^{p}\right){\rm e}^{C_{2}t}, \quad 1\leqslant k\leqslant N. $$

关键词: $p$-Wasserstein distance, Linear-Formation model, mean-field limit, propagation of chaos

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 $$ W^p_p(f_{t}^{\otimes k},f_{N,k}^{t}) \leqslant C_{1} \frac{k}{N^{\min(p/2,1)}}\left(1+t^{p}\right){\rm e}^{C_{2}t}, \quad 1\leqslant k\leqslant N. $$

Key words: $p$-Wasserstein distance, Linear-Formation model, mean-field limit, propagation of chaos

中图分类号:

60H15

Juntao WU, Xiao WANG, Yicheng LIU. MEAN FIELD LIMIT AND PROPAGATION OF CHAOS FOR LINEAR-FORMATION MODEL[J]. 数学物理学报(英文版), 2025, 45(5): 2217-2250.

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.

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