Log-majorizations for the (symplectic) eigenvalues of the Cartan barycenter

2017/10/02 by Hiai, Fumio, Lim, Yongdo · 1 citation
#15A42 #47A64 #47B65 #47L07 #FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR)

paper · doi:10.48550/arxiv.1710.00494

Abstract

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 log-majorizations for the (symplectic) eigenvalues of the Cartan barycenter of integrable probability Borel measures. This leads a version of Jensen's inequality for geometric integrals of matrix-valued integrable random variables.

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