Open Access
2013 Limiting spectral distribution of sum of unitary and orthogonal matrices
Anirban Basak, Amir Dembo
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Electron. Commun. Probab. 18: 1-19 (2013). DOI: 10.1214/ECP.v18-2466


We show that the empirical eigenvalue measure for sum of $d$ independent Haar distributed $n$-dimensional unitary matrices, converge for $n \rightarrow \infty$ to the Brown measure of the free sum of $d$ Haar unitary operators. The same applies for independent Haar distributed $n$-dimensional orthogonal matrices. As a byproduct of our approach, we relax the requirement of uniformly bounded imaginary part of Stieltjes transform of $T_n$ that is made in [Guionnet, Krishnapur, Zeitouni; Theorem 1].


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Anirban Basak. Amir Dembo. "Limiting spectral distribution of sum of unitary and orthogonal matrices." Electron. Commun. Probab. 18 1 - 19, 2013.


Accepted: 10 August 2013; Published: 2013
First available in Project Euclid: 7 June 2016

zbMATH: 1307.46049
MathSciNet: MR3091727
Digital Object Identifier: 10.1214/ECP.v18-2466

Primary: 46L53
Secondary: 60B10 , 60B20

Keywords: Brown measure , Free convolution , Haar measure , Limiting spectral distribution , random matrices , Schwinger-Dyson equation , Stieltjes transform

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