TITLE: Random Walks and Lyapunov exponents
QUESTION [10 upvotes]: Given a sequence $Y_1, Y_2, \dots$ of i.i.d. matrices in $GL_n(\mathbb R)$, there is a theorem of Furstenberg and Kesten which says that if $\mathbb E(\log||Y_1||)$ is finite, there exists a constant $\gamma$ (the Lyapunov exponent) such that
$$\lim_{n\rightarrow\infty}\frac{1}{n}\log||Y_n\dots Y_1|| = \gamma$$
There are also versions of central limit theorems for this scenario.  I'm pretty sure this is also known in a more general case (e.g. suppose we have a sequence of matrices $Y_i$ of order 2, and I don't want to consider sequences of length $n$ in which $\dots Y_i Y_i\dots$ appears).    I am wondering if anyone knows a good reference for theorems regarding Lyapunov exponents and central theorems in this case.

REPLY [2 votes]: I believe the paper
  Almost all cocycles over any hyperbolic system have non-vanishing Lyapunov exponents
  Annals of Math. 167 (2008), 643-680.

available for free at http://www.preprint.impa.br/Shadows/SERIE_A/2005/384.html contains positivity results for the Lyapunov exponent over hyperbolic dynamical systems.
Also the paper by C. Bonatti, X. Gomez-Mont, and M. Viana cited as [7] in there should be of interest.
I am not sure if they treat central limit theorems in these works.