Contributions on Non–Asymptotic Singularity of Random Matrices and on Backbend Percolation
| Autor: | PAULO CESAR MANRIQUE MIRON |
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| Jazyk: | Spanish; Castilian |
| Rok vydání: | 2017 |
| Předmět: | |
| Zdroj: | Centro de Investigación en Matemáticas CIMAT Repositorio Institucional CIMAT |
| Popis: | The main purpose of this thesis is the study of invertibility of unstructured and structured random matrices, which have been intensively investigated for at least five decades. Chapter 2 contains a brief introduction to the problem of the singularity of random matrices. Chpater 3 presents the main probabilistic tools to prove that Ginibre and Wigner matrices are invertible with hihg probability. Chapter 4 presents some of the main results in this thesis. Theorem 13 in this chapter establishes the universality rate of the probability of non--singularity of the Ginibre and Wigner matrices. Chpater 5 contains another set of the main contributions in this thesis, Theorem 14 in this chapter determines the behavior of the minimum singular value of a circulant random matrix whose entries have moment generating functions. For our proof of Theorem 14, it is used a remarkable result about the roots of a random polynomial. Finally, Chapter 6 is about our contributions on backbend percolation. |
| Databáze: | OpenAIRE |
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