Busemann Functions in the Wasserstein Space: Existence, Closed-Forms, and Applications to Slicing

ArXi:2510.04579v2 Announce Type: replace The Busemann function has recently found much interest in a variety of geometric machine learning problems, as it naturally defines projections onto geodesic rays of Riemannian manifolds and generalizes the notion of hyperplanes. As several sources of data can be conveniently modeled as probability distributions, it is natural to study this function in the Wasserstein space, which carries a rich formal Riemannian structure induced by Optimal Transport metrics.