Mixing time of Markov chains on finite and compact lie groups
Abstract/Contents
- Abstract
- This thesis studies the mixing time of three Markov chains on non-abelian groups. The first is a Metropolis Markov chain on the symmetric groups, initially introduced by Hanlon and Diaconis, and the last two are random walks on the special orthogonal groups, known as Rosenthal's walk and Kac's walk respectively. Using input from representation theory and symmetric function theory, it is shown that cut-off phenomena occur under total variation distance for the Hanlon-Diaconis chain and Rosenthal's walk. For the Kac random walk, a combination of functional-analytic and probabilistic techniques are used to establish the first polynomial order upper bound for its mixing time.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2012 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Jiang, Yunjiang |
|---|---|
| Associated with | Stanford University, Department of Mathematics |
| Primary advisor | Diaconis, Persi |
| Thesis advisor | Diaconis, Persi |
| Thesis advisor | Bump, Daniel, 1952- |
| Thesis advisor | Dembo, Amir |
| Advisor | Bump, Daniel, 1952- |
| Advisor | Dembo, Amir |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Yunjiang Jiang. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2012. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2012 by Yunjiang Jiang
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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