2022
DOI: 10.48550/arxiv.2206.02224
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On Mixing Distributions Via Random Orthogonal Matrices and the Spectrum of the Singular Values of Multi-Z Shaped Graph Matrices

Abstract: In this paper, we introduce and analyze a new operation • R which mixes two distributions Ω and Ω via a random orthogonal matrix. In particular, we take Ω • R Ω to be the limit as n → ∞ of the distribution of singular values of DRD where D and D are n × n diagonal matrices whose diagonal entries have distributions Ω and Ω respectively and R is a random n × n orthogonal matrix.We show that • R has several nice properties. We first observe that • R is commutative and associative and compute the moments of Ω • R … Show more

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