99-379 Oliver Knill

Fluctuation bounds for subharmonic functions (35K, LATeX 2e) Oct 8, 99

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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.

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