We discuss stochastic Schrödinger operators and Jacobi matrices with wave functions, taking values in
l
so there are 2
l Lyaponov exponents
1
...
l0
l+1...
2l
=–
1. Our results include the fact that if
1=0 on a set positive measure, then
V is deterministic and one that says that {
E|exactly 2
j 's are zero} is the essential support of the a.c. spectrum of multiplicity 2
j.
Communicated by T. Spencer
Research partially supported by USNSF under grant DMS-8416049