Particle approximation of nonlocal interaction energies

2025/06/03 by Carazzato, Davide, Pratelli, Aldo, Topaloglu, Ihsan
#Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2506.02905

Abstract

We consider Riesz-type nonlocal energies with general interaction kernels and their discretizations related to particle systems. We prove that the discretized energies Γ-converge in the weak-* topology to the Riesz functional defined over the space of probability measures. We also address the minimization problem for the discretized energies, and prove the existence of minimal configurations of particles in a very general and natural setting.

Citations

• Lectures on Coulomb and Riesz gases
• Aggregation-Diffusion Equations for Collective Behaviour in the Sciences
• Discrete minimizers of the interaction energy in collective behavior: a brief numerical and analytic review
• On the existence and boundedness of minimizing measures for a general form of non-local energies
• Some minimization problems for mean field models with competing forces
• Attractive Riesz potentials acting on hard spheres
• Aggregation-diffusion equations: dynamics, asymptotics, and singular limits
• Nonlocal Shape Optimization via Interactions of Attractive and Repulsive\n Potentials
• Convergence of interaction-driven evolutions of dislocations with Wasserstein dissipation and slip-plane confinement
• Regularity of local minimizers of the interaction energy via obstacle problems
• Coulomb Gases and Ginzburg-Landau Vortices

Related

• Convergence rates for energies of interacting particles whose distribution spreads out as their number increases
• Quantitative estimate of the continuum approximations of interacting particle systems in one dimension
• Explicit minimisers for anisotropic Riesz energies
• Convergence of regularized nonlocal interaction energies
• Asymptotics of k-nearest neighbor Riesz energies