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

Description
Title: Topics in Random Matrices: Theory and Applications to Probability and Statistics
Authors: Kousha, Termeh
Date: 2012
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 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.
URL: http://hdl.handle.net/10393/20480
http://dx.doi.org/10.20381/ruor-5080
CollectionThèses, 2011 - // Theses, 2011 -
Files
Kousha_Termeh_2012_thesis.pdfThesis, main article8.51 MBAdobe PDFOpen