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arXiv · 2407.18395

Wasserstein-infinity stability and mean field limit of discrete interaction energy minimizers

Ruiwen Shu
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Abstract

In this paper we give a quantitative stability result for the discrete interaction energy on the multi-dimensional torus, for the periodic Riesz potential. It states that if the number of particles $N$ is large and the discrete interaction energy is low, then the particle distribution is necessarily close to the uniform distribution (i.e., the continuous energy minimizer) in the Wasserstein-infinity distance. As a consequence, we obtain a quantitative mean field limit of interaction energy minimizers in the Wasserstein-infinity distance. The proof is based on the application of the author's previous joint work with J. Wang on the stability of continuous energy minimizer, together with a new mollification trick for the empirical measure in the case of singular interaction potentials.

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Ruiwen Shu. 2024-07-25. Wasserstein-infinity stability and mean field limit of discrete interaction energy minimizers. https://arxiv.org/abs/2407.18395

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