The Schrödinger problem on the non-commutative Fisher-Rao space (Preprint)
| <Reference List> | |
| Type: | Preprint |
| National /International: | International |
| Title: | The Schrödinger problem on the non-commutative Fisher-Rao space |
| Publication Date: | 2020-07-17 |
| Authors: |
- Léonard Monsaingeon
- Dmitry Vorotnikov |
| Abstract: | We present a self-contained and comprehensive study of the Fisher-Rao space of matrix-valued non-commutative probability measures, and of the related Hellinger space. Our non-commutative Fisher-Rao space is a natural generalization of the classical commutative Fisher-Rao space of probability measures and of the Bures-Wasserstein space of Hermitian positive-definite matrices. We introduce and justify a canonical entropy on the non-commutative Fisher-Rao space, which differs from the von Neumann entropy. We consequently derive the analogues of the heat flow, of the Fisher information, and of the dynamical Schrödinger problem. We show the Γ-convergence of the ε-Schrödinger problem towards the geodesic problem for the Fisher-Rao space, and, as a byproduct, the strict geodesic convexity of the entropy. |
| Institution: | DMUC 20-22 |
| Online version: | http://www.mat.uc.pt...prints/eng_2020.html |
| Download: | Not available |
© Centre for Mathematics, University of Coimbra, funded by
UID/00324/2025 UID/PRR/00324/2025 UID/PRR2/00324/2025 Powered by: rdOnWeb v1.4 | technical support
UID/00324/2025 UID/PRR/00324/2025 UID/PRR2/00324/2025 Powered by: rdOnWeb v1.4 | technical support