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- W4299702011 abstract "We present an approach to sums of random Hermitian matrices via the theory of spherical functions for the Gelfand pair $(mathrm{U}(n) ltimes mathrm{Herm}(n), mathrm{U}(n))$. It is inspired by a similar approach of Kieburg and Kosters for products of random matrices. The spherical functions have determinantal expressions because of the Harish-Chandra/Itzykson-Zuber integral formula. It leads to remarkably simple expressions for the spherical transform and its inverse. The spherical transform is applied to sums of unitarily invariant random matrices from polynomial ensembles and the subclass of polynomial ensembles of derivative type (in the additive sense), which turns out to be closed under addition. We finally present additional detailed calculations for the sum with a random matrix from a Laguerre Unitary Ensemble." @default.
- W4299702011 created "2022-10-02" @default.
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- W4299702011 date "2016-11-27" @default.
- W4299702011 modified "2023-09-26" @default.
- W4299702011 title "Spherical functions approach to sums of random Hermitian matrices" @default.
- W4299702011 doi "https://doi.org/10.48550/arxiv.1611.08932" @default.
- W4299702011 hasPublicationYear "2016" @default.
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