Tracial smooth functions of non-commuting variables and the free Wasserstein manifold

David Jekel, Wuchen Li, Dimitri Shlyakhtenko

We formulate a free probabilistic analog of the Wasserstein manifold on ${\mathbb{R}}^d$ (the formal Riemannian manifold of smooth probability densities on ${\mathbb{R}}^d$), and we us…