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arXiv · 1711.00433

Block-modified Wishart matrices: the easy case

Teodor Banica
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Abstract

Associated to any complex Wishart matrix $W$ of parameters $(dn,dm)$ and any linear map $\varphi:M_n(\mathbb C)\to M_n(\mathbb C)$ is the "block-modified" matrix $\tilde{W}=(id\otimes\varphi)W$. Following some previous work with Nechita, we study here the asymptotic $*$-distribution of $\tilde{W}$, in the $d\to\infty$ limit, in the case where the modification map $\varphi$ is "easy", or more generally super-easy, in the quantum algebra/representation theory sense. Under suitable assumptions on $\varphi$ we obtain in this way a compound free Poisson law.

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Teodor Banica. 2017-11-01. Block-modified Wishart matrices: the easy case. https://arxiv.org/abs/1711.00433

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