On the integrability of p-Wasserstein barycenters

par Lorenzo Portinale (Milano)

mercredi 22 avr. 2026, 10:30 → 12:30 Europe/Paris

112 (Braconnier)

We discuss the L^q integrability of the p-Wasserstein barycenters between N probability measures. It is well-known that for p=2 (as well as for N=2), as soon as one marginal belongs to L^q, the associated 2-barycenters also belongs to L^q. We consider the same problem when p is different from two, and show that in general integrability fails (for N>2), even when assuming one marginal being bounded. We also show that integrability is achieved, provided that a suitable geometric conditions on the support of the marginals holds. Various examples and open problems will be discussed. This is a joint project with C. Brizzi.