Jun-Ho Lee

Uniform-in-Time and Uniform-in-Temperature Particle Approximations of Coulomb MMD Flows

We study particle approximations of maximum mean discrepancy (MMD) flows with the Coulomb kernel on the torus $\mathbb{T}^d$, $d\ge2$, driven by thermal noise of strength $\tau\ge0$. For smooth, strictly positive initial and target densities and i.i.d. initial positions, we prove that the expected Wasserstein-1 distanc...