On nonlinear Schrödinger equations with random potentials: existence and probabilistic properties

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In this paper we are concerned with nonlinear Schrödinger equations with random potentials. Our class includes continuum and discrete potentials. Conditions on the potential Vω are found for existence of solutions almost sure ω. We study probabilistic properties like central limit theorem and law of larger numbers for the obtained solutions by independent ensembles. We also give estimates on the expected value for the L∞-norm of the solution showing how it depends on the size of the potential.