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In this paper we are concerned with nonlinear Schr\"odinger equations withrandom potentials. Our class includes continuum and discrete potentials.Conditions on the potential $V_{\omega}$ are found for existence of solutionsalmost sure $\omega $. We study probabilistic properties like central limittheorem and law of larger numbers for the obtained solutions by independentensembles. We also give estimates on the expected value for the$L^{\infty}$-norm of the solution showing how it depends on the size of thepotential.

On nonlinear Schr\"odinger equations with random potentials: existence and probabilistic properties