4 papers
On the Bures-Wasserstein distance between positive definite matrices
Rajendra Bhatia, Tanvi Jain, Yongdo Lim
The metric $d(A,B)=\left[ \tr\, A+\tr\, B-2\tr(A^{1/2}BA^{1/2})^{1/2}\right]^{1/2}$ on the manifold of positive definite matrices arises in various optimisation problem…
Log-majorizations for the (symplectic) eigenvalues of the Cartan barycenter
Fumio Hiai, Yongdo Lim
In this paper we show that the eigenvalue map and the symplectic eigenvalue map of positive definite matrices are Lipschitz for the Cartan-Hadamard Riemannian metric, and establish…
The stochastic order of probability measures on ordered metric spaces
Fumio Hiai, Jimmie Lawson, Yongdo Lim
The general notion of a stochastic ordering is that one probability distribution is smaller than a second one if the second attaches more probability to higher values than the firs…
Geometric mean flows and the Cartan barycenter on the Wasserstein space over positive definite matrices
Fumio Hiai, Yongdo Lim
We introduce a class of flows on the Wasserstein space of probability measures with finite first moment on the Cartan-Hadamard Riemannian manifold of positive definite matrices, an…