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arXiv · 2210.07434

Asymptotic free independence and entry permutations for Gaussian random matrices. Part II: Infinitesimal freeness

M. Popa·K. Szpojankowski·P. -L. Tseng
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Abstract

We study asymptotic infinitesimal distributions of Gaussian Unitary Ensembles with permuted entries. We show that for random uniform permutations, the asymptotically permuted GUE matrix has a null infinitesimal distribution. Moreover, we show that asymptotically different permutations of the same GUE matrix are infinitesimally free. Besides this we study particular example of entry permutation - the transpose, and we show that while a GUE matrix is asymptotically free from its transpose it is not infinitesimally free from it.

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M. Popa, K. Szpojankowski, P. -L. Tseng. 2022-10-14. Asymptotic free independence and entry permutations for Gaussian random matrices. Part II: Infinitesimal freeness. https://arxiv.org/abs/2210.07434

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