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- W2951208049 abstract "In this paper we prove the concavity of the $k$-trace functions, $Amapsto (text{Tr}_k[exp(H+ln A)])^{1/k}$, on the convex cone of all positive definite matrices. $text{Tr}_k[A]$ denotes the $k_{mathrm{th}}$ 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." @default.
- W2951208049 created "2019-06-27" @default.
- W2951208049 creator A5047816960 @default.
- W2951208049 date "2018-08-09" @default.
- W2951208049 modified "2023-09-23" @default.
- W2951208049 title "A generalized Lieb's theorem and its applications to spectrum estimates for a sum of random matrices" @default.
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- W2951208049 doi "https://doi.org/10.48550/arxiv.1808.05550" @default.
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