Rates of convergence of Markov chains to stationarity : strong stationary times, coupling, Gelfand pairs and comparison theory
Abstract/Contents
- Abstract
- The main purpose of this thesis is to find the mixing time for various random walks that the math community has been interested in. The methods used in this thesis are strong stationary times, introduced by Aldous and Diaconis, a coupling argument that was inspired by work of Aldous, bounding the eigenvalues of a walk via comparison theory and path arguments introduced by Diaconis and Saloff-Coste and via Gelfand pair theory developped by Diaconis and Shahshahani, but also finding the eigenvalues of random walks using Fourier Transform arguments as introduced by Diaconis and Shahshahani. There are many norms that can use to study the mixing time of a random walk on a finite group. Coupling is used to bound the $l^1$ norm, strong stationary times are used to bound the separation distance, while the eigenvalues of a reversible Markov chain are used to bound the $l^2$ norm. This thesis focuses on specific examples of Markov chains on finite spaces, some of which have been studied before but through a different norm.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2016 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Nestoridi, Evrydiki-Xenia |
|---|---|
| Associated with | Stanford University, Department of Mathematics. |
| Primary advisor | Diaconis, Persi |
| Thesis advisor | Diaconis, Persi |
| Thesis advisor | Soundararajan, Kannan, 1973- |
| Thesis advisor | Vondrak, Ján, (Mathematician) |
| Advisor | Soundararajan, Kannan, 1973- |
| Advisor | Vondrak, Ján, (Mathematician) |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Evrydiki-Xenia Nestoridi. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2016. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2016 by Evrydiki-Xenia Nestoridi
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