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Log-majorizations for the (symplectic) eigenvalues of the Cartan barycenter (1710.00494v1)
Published 2 Oct 2017 in math.FA and math.PR
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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