A generalized Lieb's theorem and its applications to spectrum estimates for a sum of random matrices

De Huang

In this paper we prove the concavity of the $k$-trace functions, $A\mapsto ({\text{Tr}}_k[\exp (H+\ln A)]{)}^{1/k}$, on the convex cone of all positive definite matrices. $\text{Tr}_k[A…