Random walks and Lyapunov exponents Given a sequence $Y_1, Y_2, \dots$ of i.i.d. matrices in $\mathrm{GL}_n(\mathbb R)$, 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.
 A: I had double checked, in the book "Products of Random Matrices With Applications to Schrodinger Operators" BOUGEROL Philippe, LACROIX Jean (chapter 5 of part 1) you will find Central Limit theorems even for markovian sequences. 
The Furstenberg-Kesten result generalizes as much as you like after Kingman's subaditive theorem. For this stuff, I like this notes http://www.mat.puc-rio.br/~jairo/docs/trieste.pdf
A: 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.
A: Random dynamical systems by Ludwig Arnold contains a thorough discussion of various multiplicative ergodic theorems (including the Furstenberg-Kesten result), but not the central limit theorems. As far as I remember, the case of stationary sequences of linear stochastic iterations is also included there.
Edit. Concerning central limit theorems for products of random matrices, a quick search yields this reference.
