Brown measure and asymptotic freeness of elliptic and related matrices

Kartick Adhikari; Arup Bose

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arXiv · 1710.08160

Brown measure and asymptotic freeness of elliptic and related matrices

Kartick Adhikari·Arup Bose

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Abstract

We show that independent elliptic matrices converge to freely independent elliptic elements. Moreover, the elliptic matrices are asymptotically free with deterministic matrices under appropriate conditions. We compute the Brown measure of the product of elliptic elements. It turns out that this Brown measure is same as the limiting spectral distribution.

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Kartick Adhikari, Arup Bose. 2017-10-23. Brown measure and asymptotic freeness of elliptic and related matrices. https://arxiv.org/abs/1710.08160

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