Asymptotic freeness of sample covariance matrices via embedding

Monika Bhattacharjee; Arup Bose

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arXiv · 2101.06481

Asymptotic freeness of sample covariance matrices via embedding

Monika Bhattacharjee·Arup Bose

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Abstract

We present an alternative proof of asymptotic freeness of independent sample covariance matrices, when the dimension and the sample size grow at the same rate, by embedding these matrices into Wigner matrices of a larger order and using asymptotic freeness of independent Wigner and deterministic matrices.

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Monika Bhattacharjee, Arup Bose. 2021-01-16. Asymptotic freeness of sample covariance matrices via embedding. https://arxiv.org/abs/2101.06481

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