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Acceso Abierto
Lyapunov Exponents to Predict the Behavior of the Product of Random Matrices
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Autores
Bermúdez Guzmán, Juliana
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Fecha
2025-06-09
Directores
Artigiani, Mauro
Martínez, Cristian
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Editor
Universidad del Rosario
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Resumen
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.
Abstract
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.
Palabras clave
Exponentes de Lyapunov , Matrices aleatorios , Caos , Teoría ergódica
Keywords
Lyapunov Exponents , Random Matrices , Chaos , Ergodic Theory
