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Local semicircle law with imprimitive variance matrix


 
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1. Title Title of document Local semicircle law with imprimitive variance matrix
 
2. Creator Author's name, affiliation, country Oskari Heikki Ajanki; Institute of Science and Technology Austria; Austria
 
2. Creator Author's name, affiliation, country Lászlo Erdős; Institute of Science and Technology Austria; Austria
 
2. Creator Author's name, affiliation, country Torben Krüger; Institute of Science and Technology Austria; Austria
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) generalised Wigner matrices; generalised random sample covariance matrices; hard edge; local semicircle law
 
3. Subject Subject classification 15B52; 60B20;
 
4. Description 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) ERC (Project RANMAT, No. 338804); German Research Council (SFB-TR 12 Grant)
 
7. Date (YYYY-MM-DD) 2014-06-09
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/3121
 
10. Identifier Digital Object Identifier 10.1214/ECP.v19-3121
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 19
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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