2024/07/25 by Ruiwen Shu, Shu, Ruiwen
Computer Science · Mathematics · #52C35 #74G65 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Markov Chains and Monte Carlo Methods
paper · pdf · doi:10.48550/arxiv.2407.18395
openalex publication_date 2024/07/25 · openalex created_date 2024/09/12 · openalex updated_date 2026/07/28
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.