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dc.contributor.advisorKrishnapur, Manjunath
dc.contributor.authorNanda Kishore Reddy, S
dc.date.accessioned2018-02-07T14:58:28Z
dc.date.accessioned2018-07-31T06:09:14Z
dc.date.available2018-02-07T14:58:28Z
dc.date.available2018-07-31T06:09:14Z
dc.date.issued2018-02-07
dc.date.submitted2016
dc.identifier.urihttps://etd.iisc.ac.in/handle/2005/3073
dc.identifier.abstracthttp://etd.iisc.ac.in/static/etd/abstracts/3938/G28254-Abs.pdfen_US
dc.description.abstractIn 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.en_US
dc.language.isoen_USen_US
dc.relation.ispartofseriesG28254en_US
dc.subjectRandom Matricesen_US
dc.subjectEigenvaluesen_US
dc.subjectRectangular Matricesen_US
dc.subjectIsotropic Random Matricesen_US
dc.subjectRandom Matrixen_US
dc.subjectHaar Unitary Matricesen_US
dc.subject.classificationMathematicsen_US
dc.titleEigenvalues of Products of Random Matricesen_US
dc.typeThesisen_US
dc.degree.namePhDen_US
dc.degree.levelDoctoralen_US
dc.degree.disciplineFaculty of Scienceen_US


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