Oliver Knill
Fluctuation bounds for subharmonic functions
(35K, 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.