Higher-dimensional mean-field limit for the singular Bessel–Yukawa particle system

Establish a quantitative mean-field limit for the deterministic particle system associated with the nonlocal continuity equation using the Bessel–Yukawa resolvent kernel on closed Riemannian manifolds of dimension greater than one, where the kernel has a Coulomb-type singularity.

Background

The paper proves global well-posedness and a uniform-in-time propagation-of-chaos estimate only on the circle, where the Bessel–Yukawa kernel is bounded but has a cusp singularity. In dimensions greater than one, the kernel has a genuinely singular Coulomb-type behavior, so the modulated-energy argument used in one dimension cannot be applied directly.

The authors indicate that truncation techniques developed for singular Coulomb and Riesz interactions may provide a route toward the higher-dimensional result. Establishing this extension would generalize the particle approximation of the regularized diffusion equation, and consequently its convergence to heat flow, beyond dimension one.