Abstract
In this paper we prove the concavity of the k-trace functions, A↦(Trk[exp(H+lnA)])1/k, on the convex cone of all positive definite matrices. Trk[A] denotes the k-th elementary symmetric polynomial of the eigenvalues of A. As an application, we use the concavity of these k-trace functions to derive tail bounds and expectation estimates on the sum of the k largest (or smallest) eigenvalues of a sum of random matrices.
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