Large powers of random matrices
Abstract/Contents
- Abstract
- This dissertation comprises five papers, concerned with Wishart and Wigner ensembles. The underlying technique for its results is the method of moments, which in random matrix theory amounts to computing expectations of traces of large powers of matrices and inferring from them properties of the eigenspectrum. The main novelties are twofold, employing trace differences, and using traces to obtain eigenvector universality for a broad family of distributions. This combinatorial approach contrasts with the prevalent means for tackling questions related to eigenspaces, local laws, which rely on resolvents and stochastic differential equations.
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 | 2023; ©2023 |
| Publication date | 2023; 2023 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Diaconu, Simona |
|---|---|
| Degree supervisor | Papanicolaou, George |
| Thesis advisor | Papanicolaou, George |
| Thesis advisor | Dembo, Amir |
| Thesis advisor | Ryzhik, Leonid |
| Degree committee member | Dembo, Amir |
| Degree committee member | Ryzhik, Leonid |
| Associated with | Stanford University, School of Humanities and Sciences |
| Associated with | Stanford University, Department of Mathematics |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Simona Diaconu. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis Ph.D. Stanford University 2023. |
| Location | https://purl.stanford.edu/qb365mr5837 |
Access conditions
- Copyright
- © 2023 by Simona Diaconu
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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