Mean-field and semiclassical limit: Wasserstein versus Schatten
Lafleche LaurentWorkshop:Optimal Transport on Quantum Struct.
on 9/29/22
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.