For a long time the standard (though not the easiest to find) reference on random matrix products was Bougerol and Lacrois:
Bougerol, Philippe, and Jean Lacroix. Products of random matrices with applications to Schrödinger operators. Birkhäuser, 1985
Given, however, that this book is almost thirty years old, I wonder if anyone can recommend a more up-to-date reference?!