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arXiv · 2209.07750

Some Limit Theorems Regarding Products of Random Matrices I: Directional Derivative of the Lyapunov Exponent

Fan Wang
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Abstract

Given an i.i.d. sequence $\{A_n(\omega)\}_{n\ge 1}$ of invertible matrices and a random matrix $B(\omega)$, we consider the random matrix sequences inductively defined by $S_n(\omega) = A_n(\omega)S_{n-1}(\omega)$ and $T_n(\omega) = B(\sigma^{n-1}\omega)S_{n-1}(\omega)+A_n(\omega)T_{n-1}(\omega)$, and study several limit theorems involving $T_n(\omega)$ as well as the asymptotic behaviour of the action of $T_n(\omega)$ on the projective space and on the unit circle.

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Fan Wang. 2022-09-16. Some Limit Theorems Regarding Products of Random Matrices I: Directional Derivative of the Lyapunov Exponent. https://arxiv.org/abs/2209.07750

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