The Oseledets basis for products of nonidentically distributed independent random matrices
The Oseledets basis for products of nonidentically distributed independent random matrices

Ilya Goldsheid, Queen Mary, University of London
Fine Hall 401
The famous Oseledets theorem states that if $g_n$ is a stationary sequence of $m\times m$ matrices then with probability 1 there is a (random) basis in ${\mathbb{R}}^m$ such that for any vector $x$ the asymptotic behaviour of $g_n...g_1x$ is the same as that for one of the vectors from this basis. The fact that the sequence is stationary is crucial for the existence of such a basis. I shall consider the case when the sequence is not stationary. It turns out that for independent nonidentically distributed matrices one can still obtain an analogue of the Oseledets's results. Some applications will be considered.