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Some remarks on the effect of the Random Batch Method on phase transition

Author

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  • Guillin, Arnaud
  • Le Bris, Pierre
  • Monmarché, Pierre

Abstract

In this article, we focus on two toy models : the Curie–Weiss model and the system of N particles in linear interactions in a double well confining potential. Both models, which have been extensively studied, describe a large system of particles with a mean-field limit that admits a phase transition. We are concerned with the numerical simulation of these particle systems. To deal with the quadratic complexity of the numerical scheme, corresponding to the computation of the O(N2) interactions per time step, the Random Batch Method (RBM) has been suggested. It consists in randomly (and uniformly) dividing the particles into batches of size p>1, and computing the interactions only within each batch, thus reducing the numerical complexity to O(Np) per time step. The convergence of this numerical method has been proved in other works.

Suggested Citation

  • Guillin, Arnaud & Le Bris, Pierre & Monmarché, Pierre, 2025. "Some remarks on the effect of the Random Batch Method on phase transition," Stochastic Processes and their Applications, Elsevier, vol. 179(C).
    • Handle: RePEc:eee:spapps:v:179:y:2025:i:c:s0304414924002060
    DOI: 10.1016/j.spa.2024.104498
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    References listed on IDEAS

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    1. Xiaojie Ding & Huijie Qiao, 2021. "Euler–Maruyama Approximations for Stochastic McKean–Vlasov Equations with Non-Lipschitz Coefficients," Journal of Theoretical Probability, Springer, vol. 34(3), pages 1408-1425, September.
    2. Herrmann, S. & Tugaut, J., 2010. "Non-uniqueness of stationary measures for self-stabilizing processes," Stochastic Processes and their Applications, Elsevier, vol. 120(7), pages 1215-1246, July.
    3. Collet, Francesca & Kraaij, Richard C., 2017. "Dynamical moderate deviations for the Curie–Weiss model," Stochastic Processes and their Applications, Elsevier, vol. 127(9), pages 2900-2925.
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