Please use this identifier to cite or link to this item:
Title: Spectral analysis of large dimentional random matrices
Keywords: large dimensional random matrices, empirical spectral distribution,Stieltjes transform, sample covariance matrices, Wigner matrices, sparse matrices
Issue Date: 7-Mar-2007
Source: ZHANG LIXIN (2007-03-07). Spectral analysis of large dimentional random matrices. ScholarBank@NUS Repository.
Abstract: Abstract: The thesis studies the limiting spectral distributionsfor three classes of large dimensional random matrices. Theyinclude the Wigner type random matrices, the general samplecovariance matrices and the sparse random matrices expressed byHadamard products.The Wigner type random matrices generalize the well known Wignerrandom matrices with independent entries to the case where theentries in the matrices are statistically correlated. The generalsample covariance matrices taking the form:$$A_n=\frac{1}{N}T_{2n}^{1/2}X_nT_{1n}X_n^*T_{2n}^{1/2},$$where $T_{2n}$ is nonnegative definite and $T_{1n}$ is Hermitian.Existing works are only available for some special cases of $A_n$,{\it e.g.} when $T_{1n}=I_n$ with $T_{2n}$ nonnegative definite orwhen $T_{1n}$ and $T_{2n}$ are both diagonal matrices. This classof random matrices of significance in many application fieldsalso. The sparse random matrices, or more specifically, theHadamard products of a (normalized) sample covariance randommatrix and a sparsing matrix, are studied under a non-homogeneousand non-zero-one sparseness assumption. The results covers most ofthe usually seen works and provides new results to the randommatrix theory.For the first two classes of random matrices, we mainly rely onthe Stieltjes transform method, while for the last class ofmatrices, we employ the moment method.
Appears in Collections:Ph.D Theses (Open)

Show full item record
Files in This Item:
File Description SizeFormatAccess SettingsVersion 
ZLX-Thesis.pdf1.1 MBAdobe PDF



Page view(s)

checked on Dec 11, 2017


checked on Dec 11, 2017

Google ScholarTM


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.