Topics in Random Matrices: Theory and Applications to Probability and Statistics

dc.contributor.authorKousha, Termeh
dc.description.abstractIn this thesis, we discuss some topics in random matrix theory which have applications to probability, statistics and quantum information theory. In Chapter 2, by relying on the spectral properties of an associated adjacency matrix, we find the distribution of the maximum of a Dyck path and show that it has the same distribution function as the unsigned Brownian excursion which was first derived in 1976 by Kennedy. We obtain a large and moderate deviation principle for the law of the maximum of a random Dyck path. Our result extends the results of Chung, Kennedy and Khorunzhiy and Marckert. In Chapter 3, we discuss a method of sampling called the Gibbs-slice sampler. This method is based on Neal's slice sampling combined with Gibbs sampling. In Chapter 4, we discuss several examples which have applications in physics and quantum information theory.
dc.publisherUniversité d'Ottawa / University of Ottawa
dc.subjectRandom matrices
dc.subjectDyck path
dc.subjectSlice sampling
dc.subjectGibbs sampler
dc.subjectBrownian excursion
dc.titleTopics in Random Matrices: Theory and Applications to Probability and Statistics
dc.faculty.departmentMathématiques et statistique / Mathematics and Statistics
dc.contributor.supervisorCollins, Benoit
dc.contributor.supervisorHandelman, David
dc.contributor.supervisorMcDonald, David
dc.embargo.termsimmediate / Science / Science
uottawa.departmentMathématiques et statistique / Mathematics and Statistics
CollectionThèses, 2011 - // Theses, 2011 -

Kousha_Termeh_2012_thesis.pdfThesis, main article8.51 MBAdobe PDFOpen