joint work with Balint Virag.

abstract:
We consider the Markov process given by products of i.i.d. random
matrices that are perturbations of a fixed non-random matrix and the
randomness is coupled with some small coupling constant.
Such random products occur in terms of transfer matrices for random
quasi-one dimensional Schroedinger operators with i.i.d. matrix potential.
Letting the number of factors going to infinity and the random disorder
going to zero in a critical scaling we obtain a a limit process for a
certain Schur complement of the random products. This limit is described
by an SDE. This allows us to obtain a limit SDE for the Markov processes
given by the action of the random products on Grassmann manifolds.