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A phase transition for the limiting spectral density of random matrices


 
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1. Title Title of document A phase transition for the limiting spectral density of random matrices
 
2. Creator Author's name, affiliation, country Olga Friesen; Westfälische Wilhelms-Universität Münster; Germany
 
2. Creator Author's name, affiliation, country Matthias Löwe; Westfälische Wilhelms-Universität Münster; Germany
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) random matrices, dependent random variables, Toeplitz matrices, semicircle law, Curie-Weiss model
 
3. Subject Subject classification 60B20; 60F15; 60K35
 
4. Description Abstract We analyze the spectral distribution of symmetric random matrices with correlated entries. While we assume that the diagonals of these random matrices are stochastically independent, the elements of the diagonals are taken to be correlated. Depending on the strength of correlation, the limiting spectral distribution is either the famous semicircle distribution, the distribution derived for Toeplitz matrices by Bryc, Dembo and Jiang (2006), or the free convolution of the two distributions.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) Deutsche Forschungsgemeinschaft (SFB 878)
 
7. Date (YYYY-MM-DD) 2013-01-29
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/2118
 
10. Identifier Digital Object Identifier 10.1214/EJP.v18-2118
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 18
 
12. Language English=en en
 
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