# Discrete one-dimensional quasi-periodic Schroedinger operators with

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We consider the discrete one-dimensional quasi-periodic

Schroedinger operator with potential defined by a Gevrey-class function.

We show - in the perturbative regime - that the operator satisfies

Anderson localization and that the Lyapunov exponent is positive and

continuous for all energies. We also mention a partial nonperturbative

result valid for some particular Gevrey classes. These results extend

some recent work by J. Bourgain, M. Goldstein, W. Schlag to a more general

class of potentials.