Field  Value 
dc.contributor.author  Kousha, Termeh 
dc.date.accessioned  20111213T19:52:37Z 
dc.date.available  20111213T19:52:37Z 
dc.date.created  2012 
dc.date.issued  2012 
dc.identifier.uri  http://hdl.handle.net/10393/20480 
dc.identifier.uri  http://dx.doi.org/10.20381/ruor5080 
dc.description.abstract  In 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 Gibbsslice 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.language.iso  en 
dc.publisher  Université d'Ottawa / University of Ottawa 
dc.subject  Random matrices 
dc.subject  Dyck path 
dc.subject  MCMC 
dc.subject  Slice sampling 
dc.subject  Gibbs sampler 
dc.subject  Brownian excursion 
dc.title  Topics in Random Matrices: Theory and Applications to Probability and Statistics 
dc.type  Thesis 
dc.faculty.department  Mathématiques et statistique / Mathematics and Statistics 
dc.contributor.supervisor  Collins, Benoit 
dc.contributor.supervisor  Handelman, David 
dc.contributor.supervisor  McDonald, David 
dc.embargo.terms  immediate 
dc.degree.name  PhD 
dc.degree.level  doctorate 
dc.degree.discipline  Sciences / Science 
thesis.degree.name  PhD 
thesis.degree.level  Doctoral 
thesis.degree.discipline  Sciences / Science 
uottawa.department  Mathématiques et statistique / Mathematics and Statistics 
Collection  Thèses, 2011  // Theses, 2011 
