Stable laws and products of positive random matrices

l Let S be the multiplicative semigroup of q x q matrices with positive entries such that every row and every column contains a strictly positive element. Denote by (X-n) n >= 1 a sequence of independent identically distributed random variables in S and by X-(n) = X-n...X-1, n >= 1, the associated left random walk on S. We assume that (Xn) n >= 1 satisfies the contraction property [GRAPHICS] where S is the subset of all matrices which have strictly positive entries. We state conditions on the distribution of the random matrix X-1 which ensure that the logarithms of the entries, of the norm, and of the spectral radius of the products X-(n), n >= 1, are in the domain of attraction of a stable law.