First-order Conditions for Optimization in the Wasserstein Space
Lanzetti NicolasWorkshop:Optimal Transport on Quantum Struct.
on 9/28/22
We discuss notions of monotone and optimal transport arising in Voiculescu’s free probability theory, related to the Biane-Voiculescu extension of the quadratic Wasserstein distance to tracial non-commutative probability spaces. In particular, we discuss the behavior of Wasserstein distance under small free semicircular perturbations and relate it to free entropy dimension and cohomology.