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dc.contributor.advisorRider, Brian (Brian C.)
dc.creatorKong, Nayeong
dc.date.accessioned2020-11-04T16:09:55Z
dc.date.available2020-11-04T16:09:55Z
dc.date.issued2018
dc.identifier.urihttp://hdl.handle.net/20.500.12613/3132
dc.description.abstractThis dissertation has two parts. In the first part, we focus on random inner product kernel matrices. Under various assumptions, many authors have proved that the limiting empirical spectral distribution (ESD) of such matrices A converges to the Marchenko- Pastur distribution. Here, we establish the corresponding rate of convergence. The strategy is as follows. First, we show that for z = u + iv ∈ C, v > 0, the distance between the Stieltjes transform m_A (z) of ESD of matrix A and Machenko-Pastur distribution m(z) is of order O (log n \ nv). Next, we prove the Kolmogorov distance between ESD of matrix A and Marchenko-Pastur distribution is of order O(3\log n\n). It is the less sharp rate for much more general class of matrices. This uses a Berry-Esseen type bound that has been employed for similar purposes for other families of random matrices. In the second part, random geometric graphs on the unit sphere are considered. Observing that adjacency matrices of these graphs can be thought of as random inner product matrices, we are able to use an idea of Cheng-Singer to establish the limiting for the ESD of these adjacency matrices.
dc.format.extent70 pages
dc.language.isoeng
dc.publisherTemple University. Libraries
dc.relation.ispartofTheses and Dissertations
dc.rightsIN COPYRIGHT- This Rights Statement can be used for an Item that is in copyright. Using this statement implies that the organization making this Item available has determined that the Item is in copyright and either is the rights-holder, has obtained permission from the rights-holder(s) to make their Work(s) available, or makes the Item available under an exception or limitation to copyright (including Fair Use) that entitles it to make the Item available.
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.subjectMathematics
dc.subjectProbability
dc.subjectRandom Geometric Graph
dc.subjectRandom Graph
dc.subjectRandom Inner Product Kernel Matrix
dc.subjectRandom Matrix
dc.subjectSpectral Distribution
dc.titleConvergence Rates of Spectral Distribution of Random Inner Product Kernel Matrices
dc.typeText
dc.type.genreThesis/Dissertation
dc.contributor.committeememberYang, Wei-shih, 1954-
dc.contributor.committeememberBerhanu, Shiferaw
dc.contributor.committeememberMukhopadhyay, Subhadeep
dc.description.departmentMathematics
dc.relation.doihttp://dx.doi.org/10.34944/dspace/3114
dc.ada.noteFor Americans with Disabilities Act (ADA) accommodation, including help with reading this content, please contact scholarshare@temple.edu
dc.description.degreePh.D.
refterms.dateFOA2020-11-04T16:09:55Z


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