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

Arnaud Guillin, Pierre Le Bris and Pierre Monmarché

Stochastic Processes and their Applications, 2025, vol. 179, issue C

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.

Keywords: Interacting particle system; Curie–Weiss model; Phase transition; Random Batch Method; McKean–Vlasov diffusion (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spa.2024.104498

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