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.



Random walks and Lyapunov exponents
*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](https://projecteuclid.org/journals/annals-of-probability/volume-25/issue-4/Limit-theorems-for-products-of-positive-random-matrices/10.1214/aop/1023481103.full).


