Oliver Knill
Fluctuation bounds for subharmonic functions
(42K, LATeX 2e)

ABSTRACT.  We obtain bounds for the angular fluctuations of a
subharmonic function in terms of the distribution of the angular
mean. As an application, we get new results on positive Lyapunov 
exponents for matrix cocycles which appear as transfer cocycles of 
discrete random Schroedinger operators and as Jacobeans of symplectic
maps.  One application shows there are no realanalytic potentials
V on the d-torus for which for fixed E and fixed but arbitrary 
volume preserving transformation T on that torus the transfer 
cocycle of the random Jacobi matrix
(Lu)(n) = u(n+1) + u(n-1) + g V(n) u(n) has a bounded
Lyapunov exponent at the energy E for g going to infinity. 
(This is a revision of mp_arc 99-379. It contains additionally 
an introduction and more references.)