Topics in Random Matrices: Theory and Applications to Probability and Statistics
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 tha...
Main Author: | |
---|---|
Language: | en |
Published: |
2011
|
Subjects: | |
Online Access: | http://hdl.handle.net/10393/20480 |
id |
ndltd-LACETR-oai-collectionscanada.gc.ca-OOU-OLD.-20480 |
---|---|
record_format |
oai_dc |
spelling |
ndltd-LACETR-oai-collectionscanada.gc.ca-OOU-OLD.-204802013-04-05T03:21:09ZTopics in Random Matrices: Theory and Applications to Probability and StatisticsKousha, TermehRandom matricesDyck pathMCMCSlice samplingGibbs samplerBrownian excursionIn 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.2011-12-13T19:52:37Z2011-12-13T19:52:37Z20122011-12-13Thèse / Thesishttp://hdl.handle.net/10393/20480en |
collection |
NDLTD |
language |
en |
sources |
NDLTD |
topic |
Random matrices Dyck path MCMC Slice sampling Gibbs sampler Brownian excursion |
spellingShingle |
Random matrices Dyck path MCMC Slice sampling Gibbs sampler Brownian excursion Kousha, Termeh Topics in Random Matrices: Theory and Applications to Probability and Statistics |
description |
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. |
author |
Kousha, Termeh |
author_facet |
Kousha, Termeh |
author_sort |
Kousha, Termeh |
title |
Topics in Random Matrices: Theory and Applications to Probability and Statistics |
title_short |
Topics in Random Matrices: Theory and Applications to Probability and Statistics |
title_full |
Topics in Random Matrices: Theory and Applications to Probability and Statistics |
title_fullStr |
Topics in Random Matrices: Theory and Applications to Probability and Statistics |
title_full_unstemmed |
Topics in Random Matrices: Theory and Applications to Probability and Statistics |
title_sort |
topics in random matrices: theory and applications to probability and statistics |
publishDate |
2011 |
url |
http://hdl.handle.net/10393/20480 |
work_keys_str_mv |
AT koushatermeh topicsinrandommatricestheoryandapplicationstoprobabilityandstatistics |
_version_ |
1716579475503710208 |