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Balanced random and Toeplitz matrices

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Balanced random and Toeplitz matrices
2.	Creator	Author's name, affiliation, country	Aniran Basak; Stanford University
2.	Creator	Author's name, affiliation, country	Arup Bose; Indian Statistical Institute
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Random matrix, eigenvalues, balanced matrix, moment method, bounded Lipschitz metric, Carleman condition, almost sure convergence, convergence in distribution, uniform integrability.
3.	Subject	Subject classification	Primary 60B20; Secondary 60F05, 62E20, 60G57, 60B10.
4.	Description	Abstract	Except for the Toeplitz and Hankel matrices, the common patterned matrices for which the limiting spectral distribution (LSD) are known to exist share a common property–the number of times each random variable appears in the matrix is (more or less) the same across the variables. Thus it seems natural to ask what happens to the spectrum of the Toeplitz and Hankel matrices when each entry is scaled by the square root of the number of times that entry appears in the matrix instead of the uniform scaling by $n^{−1/2}$. We show that the LSD of these balanced matrices exist and derive integral formulae for the moments of the limit distribution. Curiously, it is not clear if these moments define a unique distribution
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	Melvin and Joan Lane Endowed Stanford Graduate Fellowship Fund; J.C.Bose National Fellowship, Department of Science and Technology, Government of India.
7.	Date	(YYYY-MM-DD)	2010-04-27
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/1537
10.	Identifier	Digital Object Identifier	10.1214/ECP.v15-1537
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 15
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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