How to cite item

Limiting spectral distribution of sum of unitary and orthogonal matrices

   
@article{ECP2466,
	author = {Anirban Basak and Amir Dembo},
	title = {Limiting spectral distribution of sum of unitary and orthogonal matrices},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {18},
	year = {2013},
	keywords = {Random matrices, limiting spectral distribution, Haar measure, Brown measure, free convolution, Stieltjes transform, Schwinger-Dyson equation.},
	abstract = {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].},
	pages = {no. 69, 1-19},
	issn = {1083-589X},
	doi = {10.1214/ECP.v18-2466},    
        url = {http://ecp.ejpecp.org/article/view/2466}}