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2014 Local semicircle law with imprimitive variance matrix
Oskari Ajanki, Lászlo Erdős, Torben Krüger
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Electron. Commun. Probab. 19: 1-9 (2014). DOI: 10.1214/ECP.v19-3121

Abstract

We extend the proof of the local semicircle law for generalized Wigner matrices given in [4] 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.

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Oskari Ajanki. Lászlo Erdős. Torben Krüger. "Local semicircle law with imprimitive variance matrix." Electron. Commun. Probab. 19 1 - 9, 2014. https://doi.org/10.1214/ECP.v19-3121

Information

Accepted: 9 June 2014; Published: 2014
First available in Project Euclid: 7 June 2016

zbMATH: 1310.15069
MathSciNet: MR3216567
Digital Object Identifier: 10.1214/ECP.v19-3121

Subjects:
Primary: 15B52
Secondary: 60B20

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