Lyapunov Exponents to Predict the Behavior of the Product of Random Matrices
In this thesis, we investigate the asymptotic behavior of products of random matrices through Lyapunov exponents. Our theoretical framework is grounded in Kingman’s Subadditive Ergodic Theorem, from which we derive the Furstenberg-Kesten Theorem and Oseledets’ Theorem in two dimensions. These result...
- Autores:
- Tipo de recurso:
- Fecha de publicación:
- 2025
- Institución:
- Universidad del Rosario
- Repositorio:
- Repositorio EdocUR - U. Rosario
- Idioma:
- eng
- OAI Identifier:
- oai:repository.urosario.edu.co:10336/45741
- Acceso en línea:
- https://repository.urosario.edu.co/handle/10336/45741
- Palabra clave:
- Exponentes de Lyapunov
Matrices aleatorios
Caos
Teoría ergódica
Lyapunov Exponents
Random Matrices
Chaos
Ergodic Theory
- Rights
- License
- Attribution-NonCommercial-NoDerivatives 4.0 International
| Summary: | In this thesis, we investigate the asymptotic behavior of products of random matrices through Lyapunov exponents. Our theoretical framework is grounded in Kingman’s Subadditive Ergodic Theorem, from which we derive the Furstenberg-Kesten Theorem and Oseledets’ Theorem in two dimensions. These results provide the tools to quantify exponential growth rates and directional behavior in random matrix products. To visualize our theoretical conclusions, we present a series of simulations that illustrate the emergence of Lyapunov exponents and their predictive power in practical settings. |
|---|