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Joint convergence of several copies of different patterned random matrices


 
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1. Title Title of document Joint convergence of several copies of different patterned random matrices
 
2. Creator Author's name, affiliation, country Riddhipratim Basu; University of California, Berkeley; United States
 
2. Creator Author's name, affiliation, country Arup Bose; Indian Statistical Institute; India
 
2. Creator Author's name, affiliation, country Shirshendu Ganguly; University of Washington; United States
 
2. Creator Author's name, affiliation, country Rajat Subhra Hazra; University of Zurich; Switzerland
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Random matrices, free probability, joint convergence, patterned matrices, Toeplitz matrix, Hankel matrix, Reverse Circulant matrix, Symmetric Circulant matrix, Wigner matrix
 
3. Subject Subject classification Primary 60B20; Secondary 60B10; 46L53;46L54
 
4. Description Abstract

We study the joint convergence of independent copies of several patterned matrices in the non-commutative probability setup. In particular, joint convergence holds for the well known Wigner, Toeplitz, Hankel, Reverse Circulant and Symmetric Circulant matrices. We also study some properties of the limits. In particular, we show that copies of Wigner becomes asymptotically free with copies of any of the above other matrices.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) R. Basu's research is supported by Lo\`eve Fellowship, Department of Statistics, University of California, Berkeley. A.Bose's research supported by Department of Science and Technology, Govt. of India
 
7. Date (YYYY-MM-DD) 2012-09-28
 
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/1970
 
10. Identifier Digital Object Identifier 10.1214/EJP.v17-1970
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 17
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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