Abstract: Considering independently and identically distributed random products of SL(2, R) matrices, a classic result by Furstenberg states exponential growth of the matrix norm (except in some 'degenerate' cases). Another way of looking at it is to consider the linear cocycle with a Bernoulli automorphism at its base and the corresponding matrix multiplication. We surround the ‘limits of possible generalizations’ of this statement by showing that there are loosely Bernoulli automorphisms with zero maximal exponent. It is joint work with L. J. Díaz and M. Rams.
