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Uniform-in-Time Estimates on the Size of Chaos for Interacting Particle Systems

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This paper demonstrates uniform-in-time estimates on L2 norms in interacting particle systems, implying new insights into chaotic behavior.

Uniform-in-time estimates of the L2 norm of correlation functions are established under certain conditions.
Results indicate that a large enough diffusion coefficient facilitates these estimates for chaos size.
The study reveals how tighter conditions on kernel properties can alleviate initial data dependence.
Fluctuation results of the empirical measure are inferred from the chaos size estimations.

Pengzhi Xie (2025) studied this question.

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This paper demonstrates uniform-in-time estimates on L2 norms in interacting particle systems, implying new insights into chaotic behavior.