Record Details

Eigenvalues of Products of Random Matrices

Electronic Theses of Indian Institute of Science

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Field Value
 
Title Eigenvalues of Products of Random Matrices
 
Creator Nanda Kishore Reddy, S
 
Subject Random Matrices
Eigenvalues
Rectangular Matrices
Isotropic Random Matrices
Random Matrix
Haar Unitary Matrices
Mathematics
 
Description In this thesis, we study the exact eigenvalue distribution of product of independent rectangular complex Gaussian matrices and also that of product of independent truncated Haar unitary matrices and inverses of truncated Haar unitary matrices. The eigenvalues of these random matrices form determinantal point processes on the complex plane. We also study the limiting expected empirical distribution of appropriately scaled eigenvalues of those matrices as the size of matrices go to infinity. We give the first example of a random matrix whose eigenvalues form a non-rotation invariant determinantal point process on the plane.
The second theme of this thesis is infinite products of random matrices. We study the asymptotic behaviour of singular values and absolute values of eigenvalues of product of i .i .d matrices of fixed size, as the number of matrices in the product in-creases to infinity. In the special case of isotropic random matrices, We derive the asymptotic joint probability density of the singular values and also that of the absolute values of eigenvalues of product of right isotropic random matrices and show them to be equal. As a corollary of these results, we show probability that all the eigenvalues of product of certain i .i .d real random matrices of fixed size converges to one, as the number of matrices in the product increases to infinity.
 
Contributor Krishnapur, Manjunath
 
Date 2018-02-07T14:58:28Z
2018-02-07T14:58:28Z
2018-02-07
2016
 
Type Thesis
 
Identifier http://hdl.handle.net/2005/3073
http://etd.ncsi.iisc.ernet.in/abstracts/3938/G28254-Abs.pdf
 
Language en_US
 
Relation G28254