Double coset Markov chains
Abstract/Contents
- Abstract
- Markov chains and random processes are ubiquitous in statistical and scientific applications. The main contribution of this thesis is to introduce the study of Markov chains on double cosets. Given a group and two sub-groups, the double cosets define equivalence classes of the group. A random walk on the group then induces a random processes on the set of equivalence classes. When is this random process also a Markov chain? Surprisingly, some of the examples capture scientifically (and mathematically) interesting special cases. This thesis develops a general theory for double coset Markov chains. Several cases are investigated in detail. Special attention is given to the example in which parabolic subgroups of the permutation group are indexed by contingency tables. In each of the examples the general theory developed here is applied to understand the eigenvalues, eigenfunctions, and the mixing times of the Markov chains. In the second half of this thesis two more new random processes are studied: A Markov chain on a space of coalescent trees (also related to a double coset space) and an urn model with an infinite color space. The long-term behavior of each is analyzed.
Description
| Type of resource | text |
|---|---|
| Form | electronic resource; remote; computer; online resource |
| Extent | 1 online resource. |
| Place | California |
| Place | [Stanford, California] |
| Publisher | [Stanford University] |
| Copyright date | 2022; ©2022 |
| Publication date | 2022; 2022 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Simper, Mackenzie Alice |
|---|---|
| Degree supervisor | Diaconis, Persi |
| Thesis advisor | Diaconis, Persi |
| Thesis advisor | Chatterjee, Sourav |
| Thesis advisor | Palacios Roman, Julia Adela |
| Degree committee member | Chatterjee, Sourav |
| Degree committee member | Palacios Roman, Julia Adela |
| Associated with | Stanford University, Department of Mathematics |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Mackenzie Alice Simper. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis Ph.D. Stanford University 2022. |
| Location | https://purl.stanford.edu/gk263qs8388 |
Access conditions
- Copyright
- © 2022 by Mackenzie Alice Simper
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
Also listed in
Loading usage metrics...