On the mean-field limit of the Cucker-Smale model with Random Batch Method
<|reference_start|>On the mean-field limit of the Cucker-Smale model with Random Batch Method: In this work, we focus on the mean-field limit of the Random Batch Method (RBM) for the Cucker-Smale model. Different from the classical mean-field limit analysis, the chaos in this model is imposed at discrete time and is propagated to discrete time flux. We approach separately the limits of the number of particles $N\to\infty$ and the discrete time interval $\tau\to 0$ with respect to the RBM, by using the flocking property of the Cucker-Smale model and the observation in combinatorics. The Wasserstein distance is used to quantify the difference between the approximation limit and the original mean-field limit. Also, we combine the RBM with generalized Polynomial Chaos (gPC) expansion and proposed the RBM-gPC method to approximate stochastic mean-field equations, which conserves positivity and momentum of the mean-field limit with random inputs.<|reference_end|>
@article{wang2024on,
    title={On the mean-field limit of the Cucker-Smale model with Random Batch
  Method},
    author={Yuelin Wang and Yiwen Lin},
    journal={arXiv preprint arXiv:2407.21297},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.21297},
    primaryClass={math.NA cs.NA math.AP math.CA math.PR}
}