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Local semicircle law with imprimitive variance matrix

   
@article{ECP3121,
	author = {Oskari Ajanki and Lászlo Erdős and Torben Krüger},
	title = {Local semicircle law with imprimitive variance matrix},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {19},
	year = {2014},
	keywords = {generalised Wigner matrices; generalised random sample covariance matrices; hard edge; local semicircle law},
	abstract = {
We extend the proof of the local semicircle law for generalized Wigner matrices given in MR3068390 to the case when the matrix of variances has an eigenvalue $-1$. In particular, this result provides a short proof of  the optimal local Marchenko-Pastur law at the hard edge (i.e. around zero) for  sample covariance matrices $\boldsymbol{\mathrm{X}}^\ast \boldsymbol{\mathrm{X}} $, where the variances of the entries of $ \boldsymbol{\mathrm{X}} $ may vary.
},
	pages = {no. 33, 1-9},
	issn = {1083-589X},
	doi = {10.1214/ECP.v19-3121},    
        url = {http://ecp.ejpecp.org/article/view/3121}}