论文标题
关于非共同渔-RAO空间的Schrödinger问题
The Schrödinger problem on the non-commutative Fisher-Rao space
论文作者
论文摘要
我们介绍了对基质值的非共同概率度量以及相关的Hellinger空间的Fisher-Rao空间的独立和全面研究。我们的非交互性Fisher-Rao空间是对概率度量的经典Fisher-Rao空间的自然概括，以及Hermitian阳性降级矩阵的Bures-Wasserstein空间。我们在非交流性的Fisher-Rao空间上介绍并证明了典型的熵，该空间与冯·诺伊曼熵不同。因此，我们得出了热流，渔民信息和动态施罗丁问题的类似物。我们将$γ$ - $ε$-schrödinger问题的$γ$ - 融合到Fisher-rao空间的地理问题上，并且作为副产品，是熵的严格地球均匀性。
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.
