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Another look at the moment method for large dimensional random matrices

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Another look at the moment method for large dimensional random matrices
2.	Creator	Author's name, affiliation, country	Arup Bose; Indian Statistical Institute
2.	Creator	Author's name, affiliation, country	Arnab Sen; University of California, Berkeley
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Bounded Lipschitz metric, large dimensional random matrices, eigenvalues, Wigner matrix, sample variance covariance matrix, Toeplitz matrix, Hankel matrix, circulant matrix, symmetric circulant matrix, reverse circulant matrix, palindromic matrix, limit
3.	Subject	Subject classification	60F05, 60F15, 62E20, 60G57
4.	Description	Abstract	The methods to establish the limiting spectral distribution (LSD) of large dimensional random matrices includes the  well known moment method which invokes the trace formula. Its success has been demonstrated in several types of matrices such as the Wigner matrix and the sample variance covariance matrix. In a recent article Bryc, Dembo and Jiang (2006) establish the LSD for the random Toeplitz and Hankel matrices using the moment method.  They perform the necessary counting of terms in the trace by splitting the relevant sets into equivalent classes and relating the limits of the counts to certain volume calculations. We build on their work and present a unified approach. This helps provide  relatively short and easy proofs for the LSD of common matrices while at the same time providing insight into the nature of different LSD and their interrelations. By extending these methods we are also able to deal with matrices with appropriate dependent entries.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2008-04-12
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/501
10.	Identifier	Digital Object Identifier	10.1214/EJP.v13-501
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 13
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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