Fractional Sobolev processes on Wasserstein spaces and their energy-minimizing particle representations with applications

Given a probability-measure-valued process $(μ_t)$, we aim to find, among all path-continuous stochastic processes whose one-dimensional time marginals coincide almost surely with $(μ_t)$ (if there is any), a process that minimizes a given energy in expectation. Building on our recent study (arXiv:2