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- W2904656743 abstract "Let A and B be two n×n Hermitian matrices. Assume that the eigenvalues α1,…,αn of A are known, as well as the eigenvalues β1,…,βn of B. What can be said about the eigenvalues of the sum C=A+B? This is Horn’s problem. We revisit this question from a probabilistic viewpoint. The set of Hermitian matrices with spectrum {α1,…,αn} is an orbit Oα for the natural action of the unitary group U(n) on the space of n×n Hermitian matrices. Assume that the random Hermitian matrix X is uniformly distributed on the orbit Oα and, independently, the random Hermitian matrix Y is uniformly distributed on Oβ. We establish a formula for the joint distribution of the eigenvalues of the sum Z=X+Y. The proof involves orbital measures with their Fourier transforms, and Heckman’s measures." @default.
- W2904656743 created "2018-12-22" @default.
- W2904656743 creator A5053731079 @default.
- W2904656743 date "2019-01-01" @default.
- W2904656743 modified "2023-09-26" @default.
- W2904656743 title "Horn’s problem and Fourier analysis" @default.
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- W2904656743 doi "https://doi.org/10.2140/tunis.2019.1.585" @default.
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