Quantitative approximate independence for continuous mean field Gibbs measures

Many Gibbs measures with mean field interactions are known to be chaotic, in the sense that any collection of k particles n-particle system asymptotically independent, as n→∞ fixed or perhaps k=o(n). This paper quantifies this notion for a class continuous on Euclidean space pairwise interactions, main examples being systems governed by convex and uniformly confinement potentials. The distance between marginal law its limiting product measure is shown O((k∕n)c∧2), c proportional squared temperature. In high temperature case, improves upon prior results based subadditivity entropy, which yield O(k∕n) at best. bound O((k∕n)2) cannot improved, Gaussian example demonstrates. non-asymptotic, quantified via relative Fisher information, quadratic Wasserstein metric. method relies an priori functional inequality measure, used derive estimate k-particle terms (k+1)-particle distance.