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On a class of $H$-selfadjont random matrices with one eigenvalue of nonpositive type


 
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1. Title Title of document On a class of $H$-selfadjont random matrices with one eigenvalue of nonpositive type
 
2. Creator Author's name, affiliation, country Michal Wojtylak; Jagiellonian University; Poland
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Random matrix; Wigner matrix; eigenvalue; limit distribution of eigenvalues; $\Pi_1$-space
 
3. Subject Subject classification Primary 15B52; Secondary 15B30; 47B50
 
4. Description Abstract Large $H$-selfadjoint random matrices are considered. The matrix $H$ is assumed to have one negative eigenvalue, hence the matrix in question has precisely one  eigenvalue of nonpositive type. It is showed that this eigenvalue converges in probability to a deterministic limit. The weak limit of distribution of  the real eigenvalues is investigated as well.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) Polish Ministry of Science and Higher Education
 
7. Date (YYYY-MM-DD) 2012-10-04
 
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/2148
 
10. Identifier Digital Object Identifier 10.1214/ECP.v17-2148
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 17
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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